Hi Ali,
I would only stay on the SVR if your circumstances are uncertain (might you move or sell) or you are unable to get another mortgage as they aren't very competitive, they are less than the fixed rates at the moment, but more than all the trackers. What this would give you is time to investigate further to find the best deal, but if interest rates go up these will also go up, and it will go up soon(ish - definately this year, perhaps after the summer in my opinion).
You don't need to do anything or pay anything if you do nothing the mortgage will automatically go onto the SVR.
If you want to remortgage, give them a call about this, and they will be able to tell you the fees for applying, the rates etc, and the cost of the valuations that are available.
I think these range from a couple of hundred pounds for a basic valuation to about 600 for a homebuyer survey - you (probably) don't need this!
They may offer a remortgage deal, but to be honest it is worth shopping around, dependant on the value you may still be able to get a new mortgage.
Valuers look at what similar properties in the area have sold for and will use this as the basis for the valuation. They are being more conservative at the moment, but it is possible to challenge it if it is miles away if you can provide 3 other examples. Remember an estate agents price is a marketing offer and not a sale price, which the valuation is expected to reflect, the difference can be more significant now and is usually between 5 and 10% (in my opinion).
HTH
Sparky