elemoine
You may well indeed find they are tongue and groove boards, and that the skirting was put on afterwards. The only way to get a board up is to use a circular saw, with the blade depth set to the board thickness (probably 18mm) and to cut along a board joint to remove the tongue (and the groove!). If the boards have been nailed down (highly likely) and that the nails are ribbed (a series of circles around the nail to hold it in better), which is just as likely, then you will have difficulty getting them out without damaging the board unless you drill the head of the nail off using a high speed steel drill bit. You can then use a pry bar to lift the board, or you may have to punch the nails (or at least some of them) through the board into the joist to get enough leverage on an edge to lift the board. If you start with a board that does not have any edge under the skirting board this will make it easier to get those boards out last without removing the skirting.
I have found that the best screws to use to secure the boards are Spax screws. Well worth the extra cost of a box of these to really secure the boards.
But before you do that ensure that the problem is not the joist itself, as described previously. Personally, as I do each creaky room in my (1990) house I am changing the boards for ply, which is much better than chipboard.
As for the stairs, if you can get in underneath them then you can use similar screws to secure each tread and riser. If you cannot get in beneath, then you can drive screws in at an angle at the back of each tread if you drill a pilot hole and countersink, but only if you are going to carpet which will hide your handy work. I also plan to gripfill each joint, which will really make it solid.
I did post on another thread about another squeaking problem which I had, which turned out to be the sole plate at the base of the partition wall, which was held rigid by the other studding within the wall, but the floor beneath it was flexing up and down as people walked by....the sole plate only had 2 x 6" nails over a 9 foot length of wall attaching it to the joists through the floor. Where I removed the internal wall on one side I found this problem and placed long spax screws through the sole plate into every joist. This tightened everything up before replacing the plasterboard. If you are not removing the plasterboard then you can get away with either removing the skirting and driving long screws in at an angle through the sole plate, or you can remove carpet and if the gap is big enough you can slide a hacksaw blade in and 'count' the nails and if you find only one or two like me, cut through them to prevent the squeaking and then force something like Gripfill in between sole plate and floor to secure everything. This I found tricky to do using a sealant gun applicator, Gripfill and a McDonalds straw to reach right under the sole plate! Did the trick though, even though the pressure required on the gun left my hands aching for days!!!
I can't personally believe that building regs allow them to produce floors in this manner, as it so obviously suffers from squeaking from a very early stage.