For convenience, here are the relevant passages:

(Chapter 43, Miss Crawford's letter.)
"Henry ... cannot anyhow be spared till after the 14th, for we have a party that evening. ... He will see the Rushworths, which own I am not sorry for—having a little curiosity, and so I think has he—though he will not acknowledge it.”

(Chapter 44, Edmund's letter describing what he saw at Mrs Fraser's party.)
"... There was marked coolness on [Maria's] side. They scarcely spoke. I saw [Henry Crawford] draw back surprised, ... "

(Chapter 45, Mary's letter, received around the end of April, when Henry C returns from Richmond.)
“I had actually begun folding my letter when Henry walked in ... Mrs. R. knows a decline is apprehended; he saw her this morning: she returns to Wimpole Street to–day; the old lady is come. Now do not make yourself uneasy with any queer fancies because he has been spending a few days at Richmond. ... [Henry] repeats, and more eagerly, what he said at Portsmouth about our conveying you home ... "

(Chapter 46)
"A most scandalous, ill–natured rumour has just reached me, and I write, dear Fanny, to warn you against giving the least credit to it, should it spread into the country. ... If they are gone, I would lay my life they are only gone to Mansfield Park, and Julia with them. ..." [Mary's letter, received a week after the one in Chapter 45]

“it was with infinite concern the newspaper had to announce to the world a matrimonial fracas in the family of Mr. R. of Wimpole Street; the beautiful Mrs. R., ... having quitted her husband’s roof in company with the well–known and captivating Mr. C., the intimate friend and associate of Mr. R. ...” [From the newspaper]

(Fanny's/ON's summary, Chapter 47)
"Mrs. Rushworth had gone, for the Easter holidays, to Twickenham, with a family whom she had just grown intimate with ... to their house Mr. Crawford had constant access at all times. ... Mr. Rushworth had been gone at this time to Bath, to pass a few days with his mother, and bring her back to town, and Maria was with these friends without any restraint, without even Julia; ... Very soon after the Rushworths’ return to Wimpole Street, Sir Thomas had received a letter from an old and most particular friend in London, who hearing and witnessing a good deal to alarm him in that quarter, wrote to recommend Sir Thomas’s coming to London himself, and using his influence with his daughter to put an end to the intimacy which was already exposing her to unpleasant remarks, and evidently making Mr. Rushworth uneasy.

Sir Thomas was preparing to act upon this letter ... when it was followed by another, sent express from the same friend ... Mrs. Rushworth had left her husband’s house: Mr. Rushworth had been in great anger and distress to him (Mr. Harding) for his advice; Mr. Harding feared there had been at least very flagrant indiscretion. The maidservant of Mrs. Rushworth, senior, threatened alarmingly. He was doing all in his power to quiet everything, with the hope of Mrs. Rushworth’s return, but was so much counteracted in Wimpole Street by the influence of Mr. Rushworth’s mother, that the worst consequences might be apprehended.

... Sir Thomas set off, Edmund would go with him, and the others had been left in a state of wretchedness, inferior only to what followed the receipt of the next letters from London. Everything was by that time public beyond a hope. The servant of Mrs. Rushworth, the mother, had exposure in her power, and supported by her mistress, was not to be silenced. The two ladies, even in the short time they had been together, had disagreed; and the bitterness of the elder against her daughter–in–law might perhaps arise almost as much from the personal disrespect with which she had herself been treated as from sensibility for her son.

... But had [Maria] been less obstinate, or of less weight with her son, who was always guided by the last speaker, by the person who could get hold of and shut him up, the case would still have been hopeless, for Mrs. Rushworth did not appear again, and there was every reason to conclude her to be concealed somewhere with Mr. Crawford, who had quitted his uncle’s house, as for a journey, on the very day of her absenting herself."

Here is my version of What Happened based on the above chapters:

1) The party: HC was pressed to attend the party on 14th of April, where HC met the resentful and cold Maria.

2) The aftermath of the party: Not being able to bear to be thrown off, HC "began the attack, and by animated perseverance had soon re–established the sort of familiar intercourse, of gallantry, of flirtation". This takes place in London, I suppose, because at this time, Maria would still have Mr Rushworth and other people around her side.

3) Holidays: From the very first sentence of the Chapter 47 quote, we see that Maria finally seized the opportunity to be quite alone with HC around Easter for a few days while Mr R was not there. How intimate they have become can only be speculated; on the other hand, though it was a matter of a few days, closer reading seems to suggest that their intimacy have gone further than mere flirtation, the mention of the Twickenham family's flexible morals. Besides, there is always the Twickenham house the Admiral owned, as mentioned by Jenny Allan.

4) Holiday's over:
i) We were told that Mr and Mrs R senior has gone back to London. Maria would have had to go back to London, and ON tells us that Maria and Mrs R senior doesn't get along, "even in the short time they had been together". (Isn't this the first time Maria and Mrs R senior really got to live under the same roof?)
ii) From Chapter 48, HC was said to have been very glad to end the whole thing by this time, and thus tried to find excuse by offering Fanny to convey her to MP.
iii) Speculation: In the mean time, the flirtation still continued on in London, which I suspect come from Maria's "imprudence" JA spoke of in Chapter 48. Maria's frustration with both of the Rushworths have made her more desperate for HC's company. Mr Harding (the London friend) warned Sir T about Maria's indiscrete behaviour at Wimpole street drawing unpleasant remarks. The Power of Exposure Mrs R senior's maid servant had would likely have been obtained from this period, perhaps by catching them kissing or something. I would imagine HC had to keep up the appearance of things with Maria, before he could get a good excuse to flee. Thus he kept flirting with Maria while waited for Fanny's reply about her wish to be taken to MP.

5. A few days (or less than a week) after the return to Wimpole street:
i) At this time, the Crawfords would have definitely received Fanny's crucial reply refusing to be conveyed. HC lost the chance to get away, which he has been so desperately depended upon.
ii) Speculation: I am inclined to think that it's about the same time Fanny's letter arrived, that Maria came to apply for HC's assistance. I am also more inclined to think that Maria came in person, and without warning. Because HC had only just learnt Fanny's disinclination and Maria had come so sudden which must have took him by surprise, that he had no time nor chance to extricate himself from all this mess. Thus, he had little choice but to run away with Maria.