Analysis.

(Remember: this analysis is particularly true about British language and culture, though mostly it is the same for other English-speaking countries like Australia and the United States.)

Sentence by Sentence analysis.

Dear Mr Blake;

This letter serves as official confirmation that I am tendering my resignation from Biscuit Investments, effective immediately.
(Sally does not express any regret that she is leaving - which would be a normal courtesy.)

As you know, either party can opt out of our employment agreement provided that a month's notice is given. As I am due six weeks leave, which I am now taking, this will serve in lieu of notice.
(Again, Sally does not ask for agreement from Mr Blake, which would be more polite - instead she says what will happen.)

Regarding this contract, I have had my attention strongly drawn to the fact that I have agreed not to undertake any stock trading on behalf on any clients of Biscuit Investments for a period of three months after the termination of my employment, and you may rest assured that I intend to honour this obligation to the letter. However, your suggestion that none of these clients may do business with any firm in which I am a partner is unfounded, and according to my legal advice, an untenable position in law.
("Strongly drawn" is English understatement - it suggests that Sally was threatened by Mr Blake
The words "to the letter" are significant. It indicates that Sally will do exactly what the agreements says. However, if she can find a way to get around the intention of the agreement, she will do that.
Sally mentions "legal advice" to let Mr Blake know that she has seen a lawyer.)

Furthermore, I understand from Paul Bascombe that with the departure of myself and Mr English, Mr Barwell has decided to take early retirement, and the department for which I formerly worked is to be closed, making Bascombe redundant. Therefore the clause which specifies that I am not to enter a business which directly competes with Biscuit Investments does not apply.
(Here Sally gives an example how she intends to do as her agreement says, but will try to get around the intention.)

In the light of the unpleasant scene which ensued when news of my intended departure became known, I do not intend to return to the company to clear my desk, and I would be grateful if any personal items are forwarded to English & Dodd Plc, at the above address.
(Sally does not say what the "unpleasant scene" was, which suggests that Mr Blake already knows - in fact he was probably a part of it.)

Since I do not forsee the need for any further personal communication between us, I and Mr English take this opportunity to wish you and Biscuit Investments the success you deserve in the future.
(Sally starts by saying that she does not want to hear from Mr Blake again - this is intended to be insulting. The "success you deserve" is not the same as "good wishes" as Sally probably feels that Mr Blake's company deserves no success at all.)

Yours truly
(The usual ending here would be Yours sincerely, but Sally chooses this slightly different way to sign off to show she really does mean what she has written.)

Sally Dodd

SUMMARY

Sally announced that she was leaving Mr Blake's company to go into partnership with Ivan English. Mr Blake was furious, and he and Sally had a fight. Sally was threatened with legal action if she took any of Mr Blake's clients with her to her new company, English & Dodd. Sally is furious, and has consulted a lawyer, who has told her exactly how many of Mr Blake's threats are serious, and how she can get around them while not breaking the agreement she signed. She has left the company and does not want to go back, even to take her personal things from her desk. She is supposed to work another month, but she has said that she will take this time as holidays which she is owed. Her letter is written because she has to resign officially. It is cold and formal, and makes only a minimal effort to be polite. We learn from the letter that without Sally and Ivan, Biscuit Investments have decided to close the department where they worked, so Paul has lost his job. Sally is obviously not upset by this (notice that she calles Paul by his surname "Bascome" without any title such as "Mr").