Thanks for the tip. I called London & Country and they have been very efficient. I've gone with a 5 year fix for 3.05% from Barclays, which is only 0.05% less than going direct - but I'm happy enough with the deal, and it's fee-free.Check a broker like London and Country.
Also, don't wait. You can apply and lock in a rate with another lender usually up to 6 months in advance. As long as you have your mortgage offer, you are good. I did this in December and then waited to complete until my fix expired last month (now locked in for 5 yrs at 1.27%).
They say the rate is secured for up to 6 months, but we shall see... from experience, i know that only the mortgage offer is the legally binding thing you can rely on, and generally those are only valid for 3 months from date of offer.