You really have to smile when someone says 'yes, you can DIY, its all online' but then doesn't lift a finger to say any more than that.
Yes, it is possible and I have done it as a layman twice now. I am entirely self-taught in land law (which I only started after being seriously let down by the legal profession that seems to do a great job at looking after its own). So I sorted my own problem out and got the solicitor at fault to pay through the nose out of his indemnity policy.
If the transaction is simple - so for example there are no strange restrictions or easements associated with the land and the transaction is between two people who trust one another (such that the due diligence associated with Standard Enquiries can be dispensed with) then the heart of the matter is a document called a TR1 by the Land Registry (Google it). This is a deed, which both parties sign and is witnessed, which LR accepts as the document that it uses to register the title of the land into the name of a new proprietor.
There is an awful lot of learn - even to get that far - and I'm not sure that it is worth £350 of your time - depends on how you value your time. The LR are very helpful with laypeople and will patiently answer questions, but they won't do it for you.
In terms of background, you might like to peruse this site
http://freeconveyanci...fer-of-equity-kit.php
I'm not recommending it - I Googling for it - the same as ladybirder could have done for you. It costs £150 for the kit - which is less than £350 - but it would give you a step-by-step approach. It unfortunately covers examples of a lot more than you would need. What I was really looking for was a £20 book for you - maybe there is one but I couldn't find it in 5 minutes of searching.
Finally, have you considered the Stamp Duty Land Tax implications? - payable in steps over £40k, though free to most first-time buyers for a little longer, I believe. Just because the transfer is between relatives doen't avoid that I'm afraid. Your friend may be intending to sell it to the son for a small notional sum to avoid all this - certainly possible - but don't forget the 'gift with reservation' implications. But that's another story, and probably another question for AB.