I would actually suggest otherwise. I WOULD consolidate the loan to the mortgage
The fact that it will be secured against the property doesn't really mean anything. Your mortgage has been secured against the property for the last 20 years and has this worried you that it is this way? Unless you plan to default on the loan or mortgage you are in the exact same circumstances as you have always been.
If the loan will save you £1000 then to take the whole loan on a fixed rate will cost very very little more...maybe £10.
Because of the size of the loan the chances are you are going to source a Fee Free mortgage which means no arrangement fees, no legal fees, no valuation fees.
The only danger with this loan that I see is finding a lender that would be prepared to do it for you. I am assuming the total of the loan and mortgage is a small value (less than £25,000) and you have already said that the term is short (less than 8-10 years). Most lenders will not want to get involved with this but speak to your own lender as they may be able to help...although they may not be able to offer a fixed rate.
I wouldn't even worry if you have to go onto the lenders variable rate, if interest rates rise on this it will have a minimal impact on the loan repayments with the loan being so small.
In short, if you can get a fee free loan (look for standard variable rate mortgage or specific fee free loan) with no fees at all then I think this would work out for the better for you