Are lenders reluctant to offer mortgages on house with annexes?
It is true that some lenders do not like properties with an annex because of the potential for unauthorised tenants to obtain rights of occupation. These rights could make it very difficult for the lender to sell the property should they ever take possession. Whether it is a problem for your buyer will depend on who they have applied to for a mortgage.
What can I do?
Depending on the size of your property and whether the annex is attached or a separate building there is very little you can do to help the situation. If it is possible you could split the title so that the annex and the main building are separate legal entities. This would also depend on whether access to both properties can be maintained either physically or by granting rights of access over a shared driveway and also on whether the utility services can be split. Alternatively you could convert the annex back into part of the main building and perhaps the easiest way of doing this would be to put in connecting internal doorways without locks.
However, you could avoid all of this if your buyer approaches the right lender and this is where a good independent mortgage broker such as John Charcol can help.