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@wvm
Impossible to answer in one hit but some food for thought.
Overpaying your current mortgage is probably the best bang for buck for spare cash (assuming you can't find a better interest rate for savings compared to that on your mortgage).
You can probably borrow up to 80% of the value of your current flat assuming the likely rental income covers 125% of the interest payments on that loan.
If your equity is better than say 40% of the value of your flat you can remortgage to free up the equity and you've pretty much got your deposit for the next home straight away.
Someone else takes over paying your mortgage on flat 1.
Assuming you are paying tax and will be declaring the income from the rental property to the taxman, you may want to keep the income to a minimum. Depending on your tax bracket, profit from the rent could be as much as halved by the time you pay tax on it which hurts like hell! So, although you will pay a higher interest rate on a BTL mortgage, by the time tax has been taken into account, it probably is better, as Dammit suggests, to max out on the mortgage on the rental property. It's also worth buying in joint names as the profits can be shared as can future capital gains.
It's also worth investigating whether your current 1 bed flat is the best choice for renting. This means looking at stuff like yield i.e. annual rental income as a % of the flat's value.
usual caveats