How soon can I secure a mortgage deal?

Hello

We bought a house in September with a 20% deposit, 2 year fix at 3.99%. Not the best deal around, partly because I am self-employed, and also because of the small-ish deposit (we wanted to keep our flat and rent that out).

By the time the two years are up, we are hoping to be able to get a much better deal, due to a combination of several factors-

I will have been self-employed for nearly four years by then, which opens me up to more lenders
We have spent a lot of money doing up the place, which will hopefully reduce the LTV (place was a tip when we bought it)
Additional money available to pay down the mortgage

When can I start looking for a new deal? Do I have to wait until the two years are up, or can I secure the new rate a few months in advance? There are large fees for redeeming the mortgage early, presumably these would still apply if I changed to a new deal with the same lender?

We are just keen to lock in a good long term deal as soon as we possibly can, before house prices drop and reduce our LTV :)

Thanks in advance