Welcome to Just Answer and thanks for asking for me.
I am afraid to advise that even just by transferring the flat into your sons names, this will trigger a capital gain liability, which will be initially the market value at the time of transfer from which you can deduct the purchase price - so an initial gain of £37,000.
However from this £37,000 you can deduct the costs to buy (so legal fees) and any capital improvements made to the property (such as new kitchen and new bathroom) then with any remaining gain, for each of you and your wife, the first £10,600 will be exempt, as this is your capital gain exemption allowance.
Any remaining gain will then be liable to either 18% or 28% or a mix of both.
The rates at which capital gain tax are paid are as follows.
If either of your annual incomes are in excess of £42,475 - then the gain will be liable to 28%. If each of your annual incomes is less than £42,475 (which seems to be the case) then first you establish what unused basic rate band you have, which will allow an amount equivalent to that unused amount, to charge capital gains at 18% and any remaining gain at 28%.
For example annual income of £32,475 - means there is £10,000 unused basic rate band - so the first £10,000 of the share of the gain (after the costs and capital improvements and annual exemption allowance have been applied) will be charged at 18% and any remaining gain at 28%.
I should also alert you to the position of Inheritance tax, which could be an issue, if neither you or your wife survive more than 7 years from the date of making the gift, as it will then have to be added back into your estates for consideration of Inheritance tax.
Of course this will only be an issue if either of your estates is in excess of £325,000 and of course if you survive more than 3 years but less than the full 7, then taper relief is applied to the Inheritance tax thereby reducing it further.
I have added a table here that details how the taper relief is applied.
Taper Relief reductions
Time between the date the gift was made and the date of death
Taper relief percentage applied to the tax due
3 to 4 years
4 to 5 years
5 to 6 years
6 to 7 years
But you should alert HMRC of the transfer as soon as it is effected, so you can report any gain on your self assessment after the year end.
Do feel free to ask any follow up questions