If your bought your house for £100k, but your outstanding mortgage balance is £80k, you have £20k equity that you’ll be due back if you sell your house. If your house sells for more than you bought it for, you can add the difference on to your equity - so say it sold for £110k, you’d expect £30k back from your sale.
if you want to then buy a property for £300k, you can use that £30k as a deposit on the new property. If you also have savings, you can top up to a higher deposit by adding savings to that £30k figure.
However, you will also need to factor in costs for Estate Agents to market and sell your property, Lawyers fees to manage your sale and also your purchase, stamp duty costs, and removal company costs if you need one. As a pp has said, there may also be an early redemption fee to pay on your mortgage if you’ve “fixed” for a number of years and want to take out a new mortgage with a different lender.
We’ve recently gone through it and legal fees were circa £4k. You can use a stamp duty calculator online to check the stamp duty you’d pay (the amount due changes depending on value of your purchase,) and estate agents fees for us were 0.9% of selling price of house, plus a marketing fee (Rightmove etc) of £400 plus a home report fee (Scotland) of circa £400.