Of course you can, it’s your money (minus the dreaded fees and moving costs ☹️) make sure you are out of any fixed rates when you’re ready to move as they can incur a penalty. It’s usually a percentage of the mortgage for each year outstanding eg: if your mortgage has 3 years to run until the fixed rate finishes, its pretty standard to pay 3% of the mortgage at 2 years 2% and so on.
Have you put the 10k in a help to buy isa or anything? Don’t know fully but there was some controversy about people not being able to use the balance for deposits but it can go towards fees etc. They might have changed it now.
You’ve done amazing to save that much. If you’re using it to move, maybe speak to a financial advisor about the pros and cons of chucking it on the mortgage now to save on interest. Most Mortgage policies allow you to overpay by about 10% a year.
There is an overpayments calculator on Money Expert which is good, it will also give you a projected balance in the coming years so you’ll have an idea of what equity you’ll have to play with.
Economists and estate agents are forecasting a drop in prices this year, estimates have been between 3% and 13%. As long as you have enough to cover the deposit and fees on your next place this could mean your £220k might go further.
Have a look on banks mortgage calculators, they’re pretty good to give you facts and figures. You can play with prices, deposits and the term.
Take what you think your house is worth, knock off the discretionary 5% for negotiation, minus what the outstanding mortgage balance is, add the savings, deduct moving costs and fees, divide the figure by 1.5 and I think this should give you how much you have for a 15% deposit 🤔 😆