Hi Paul
Sorry, I'm not from moneysupermarket, but I am a qualified adviser. I have a customer in a similar situation. Here's what we are doing.
1. Remortgage existing house, converting to a Buy to let mortgage and borrowing a bit extra to raise the deposit to put down on the next house.
2. Take a mortgage on the new house with a lender comfortable with the situation with the old.
Easy so far, but there are a few factors that will affect things.
a. The rental income on the old house must be sufficent to support a Buy to let mortgage. usually this will be a surplus of about 25% on income over the mortgage payment.
b. To make is feasible, you really need to be able to raise a 25% deposit for the next house - there aren't many good rates with smaller deposits.
c. Hopefully your income is sufficent to support the new mortgage.
And, just as a note from personal experience - Nationwide would make it hard work for you.
Good luck, Hope that helps a bit.
Adrian