IIRC this question was on last years paper, the way I would answer would be as follows.
1, Legal transfer of land made correctly to the trustees however the creation of the express trust fails due to it not being in signed writing as required by Section 53(1)(b). Therefore one of three possibilities, the trust fails so B and C take legal title without being subject to a trust, the trust fails so property reverts back to Alan or the trust fails but a resulting trust arises in favour of David. The first would be unconscionable as it would be clearly contrary to the will of the settlor for B + C to claim to be outright owners, and the third pretty much ignores the statute which it is not open for the courts to do. Therefore the best explanation (and the one I think we should go with) is that B + C can choose to exercise the trust in favour of David and if they do that then Alan cannot complain, but if they choose not to do this then a resulting trust arises in favour of Alan which means the property reverts back to him.
2, For the second part therefore Alan has a beneficial interest which he can choose to alienate if he wants to. 53(1)(c) of the LPA 1925 states that dispositions of equitable interests must be made in writing and Grey v IRC confirms this (although that case is pretty unsuprising and actually doesn't really say anything additional to the statute, it was argued on a now irrelevant point on the meaning of diposition and how it was carried forth into the 1925 act). However in Vandervell (NO.1) where the beneficiary directed the trustees to transfer legal and equitable title together it was held that this did not activate section 53 and therefore did not need to be in signed writing. Unfortunately the House of Lords did not explain why this was the case and as such there has been a lot of speculation as to possible explanations. The best is the overreaching explanation of Prof Nolan which you can find in his article, it makes good sense but unfortunately as of yet there isn't any case authority for it being the correct approach. For the moment, and for this problem, I think its best just to be aware that Vandervell is good law on this point rather than worrying about why.
As B + C are already legal title holders to the land there is not a 53(1)(b) point because they have carried the transfer out using a memorandum. The way I see it is that Alan is exercising his Saunders and Vautier rights in having the property transferred to Edward and there isn't a need for an agency arguement. Besides these facts are almost identical to those in Vandervell (No.1) and so we know its something that is allowed.
3, The long standing maxim is that equity will not perfect and inperfect gift. Case law on this really stems from Milroy v Lord but over the years the maxim has been substantially eroded by cases such as Re Rose, Pennington v Waine etc. . which I shall discuss now.
Re Rose is an exception whereby the court will perfect the gift when the individual giving it has done all that is within there power to effect the transfer but the transfer is dependant on the actions of a 3rd party which had not been yet carried out. If the transfer deeds are still with the donors agent (solicitor in this case) then you have not done everything within your power to make the transfer and hence Re Rose cannot perfect the gift. Pagarini won't help either, that concerns a different point. The case you need to look at is Pennington v Waine where the court of appeal felt able to complete a gift that had been interupted by the death of the donor on the grounds that it would have been unconscionable for the gift to be revoked at that point. Unfortunately the ratio of the case did not give a clear indication of at what actual point during the process it would have been unconscionable to revoke the gift and it seems likely that the case was decided the way it was to give the most desirable result in the circumstances and that had the donor not died then it would have been decided the other way. Nevertheless it remains part of the law and therefore must be considered. I've thought up a couple of possible points and which unconscionability could arise, intention to create the gift, attempt to make the gift, the donee receiving knowledge of the gift, the donee having a legitimate expectation of receiving the gift and the donee relying on the gift to their detriment. I really can't tell you which one is correct thats for you to discuss and make an arguement about, my thoughts are either legitimate expectation or detrimental reliance which slight favour on legitimate expectation because it fits the facts of the case better. In my opinion though the case was wrongly decided and the court of appeal should have tried to find another route to achieve the desirable end or else allow the gift to fail.
I hope that helps feel free to make any comments or disagree with anything that I've said.