Your last sentence is how it is, banks have tighter lending standards and are worried about another collapse as well as having a lack of funds to provide the mortgages.
However the crisis will abate, and whilst the BofE base rate will increase, it is likely to be slowly as they will not want to cause a shock to the system that can drag us back down (as well as the Gov't hoping to inflate some of our debts away), I can see it being a good couple of years before the BBR is at a more normal level, so I think it would be cheaper in that period to stay on the SVR.
By that time, although the fixed rate deal would likely to have increased as well, the difference between those rates and the SVRs I think will be reduced and you would have benefited from 2 years at a lower rate rather than fixing higher now, and then having to fix again. Lending standards should have loosened a bit and competition will return to the market. Also, although there may be a 2nd dip in house prices, 2 or so years down the line I think the market will hopefully have stabilsed and prices will be back on the up which will reduce your LTV and you will be more likely to get a better deal, which will be supported if your current mortgage is a repayment mortgage as you will also have paid some debt off.
So I am more or less saying that you should be ok on the SVR for the next year or 2, or at least I hope so as that is what I am doing

. If I was to fix on anything, it would be on a 5 year rate, but then that is even more expensive.
I should point out though that the markets/Gov'ts/banks often surprise or are irrational, and that is why I have a lot of shoulds, thinks and maybes in what I have said. Also, there is a big risk coming up a few years down the line with the scheduled ending of the BofE liquidity facility, when that goes the banks will have not enough to lend with, but I would hope that something will be in place by then, either for it to be phased out gradually, or the part return of the wholesale/securitisation markets.
Also, I am not an expert, but I have recently changed roles at work and am now looking at the UK mortgage/housing market, and that is just my feel on what will happen, but being new to it, prehaps I am just naive.