Hi Maud,
Complicated question as so many factors to consider.
Yes you can do a transfer of Equity and you would need a solicitor to do this. Solictors will need to carry out a Bankcruptcy search usually depending on practice methods and your current lender.
Before carrying out this I would speak to your local Land REgistry to ensure that there is no restriction secured against your property. This could be either a sole propietor restriction (i.e not one owner aloud without consent of the courts) or a management Company restriction is you do not hold the freehold to your house. i.e if you pay Ground Rent of Service Charge. These do not necessarily stop you from doing the Transfer but could delay it. These are not 2 uncommon but have a look in your Title Deeds if you have them for OFFICES COPIES and check through, these tend not to be 2 hard to go through.
Also before speak to solicitor I would check with your lender to see if they are ok, usually they will be but may increase monthly payments or want to check Mrs Wage slips etc.
I would also becareful if you intend to declare yourself bankrut soon after you have completed the TOE as Official Copies from the LAnd REgistry show the date of the last Transfers and this maybe taken into consideration as clear breach of trying to avoid repossesion.
Best think id say is get some Independent Legal Advice as its complicated, hope this helps.