The funding government has available is from taxation.
Not necessarily true. Though I don't generally believe in it, there are some interesting anecdotes in Modern Monetary Theory which illustrate the belief that the purpose of tax is to create demand for government money. Government first prints money, as much as it likes, they only need a printer, then to force people to let them buy stuff with it, they pass a law requiring taxes to be paid with said money. That gives the money value. (Not entirely sure this is relevant or true for the UK today, but the historical examples where this can be clearly seen are fascinating.)
A more general reason why the statement is wrong is that government can get money from borrowing, or from just printing it.
And no, you don't need tax money to repay borrowing. Borrowing does not necessarily have to be repaid, ever. As long as the total amount of debt is growing at a slower rate than the size of the economy, apparently it's not a problem for the debt to keep on increasing.
There is a limit on how far government can go with just printing money, overdoing that will cause inflation and/or loss of confidence in the currency. I think governments all prefer increasing borrowing to printing money because it gives the currency more credibility if it looks like they're exercising some self-discipline.
Theory aside, the cost of COVID will most likely be covered by long-term (30-year) government debt. I doubt there will be large tax increases, but I suppose there will be less government spending on other things over the next 30 years, than there would otherwise have been.