TL;DR: If the gain was made within an ISA, no CGT will be due, whatever you do with the money. You can keep it in the ISA (by reinvesting in other stocks) or withdraw it to "a normal bank account"1.
First, it should be noted that the chance of your shares increasing in value ten-fold (in a reasonable time period) is very remote... it would need a 26% rise every year for 10 years to do this. Even over a "working life-time", it would need a sustained growth of about 6% for 40 years. And, of course, by then the tax-system could have changed out of all recognition!
That aside, you are correct that any gains on investments within an ISA are tax-free. As the Full ISA Guide on Money Saving Expert includes:
Tax benefits of a stocks & shares ISA:
Placing investments inside an ISA wrapper provides three tax advantages:
No tax on profits. You don't have to pay any capital gains tax on profits made from share price increases.
Invest outside an ISA and any profits made above the annual capital gains tax allowance (£12,000 for 2019/20) would be subject to tax at 10% for basic-rate taxpayers and 20% for higher-rate and additional-rate taxpayers. You make a profit when you sell a share for more than you bought it for.
No tax on interest earned on bonds. You get to keep it all.
No tax on dividend income. Inside an ISA, you don't pay tax on dividends. Outside an ISA, you'd get a £2,000 dividend income allowance, and above that basic-, higher- and additional-rate taxpayers would pay 7.5%, 32.5% and 38.1% respectively.
Capital Gains Tax is (normally) payable when you realize a gain (i.e. sell an asset that has gone up in value). As HMRC puts it on their Capital Gains Tax page:
Capital Gains Tax is a tax on the profit when you sell (or ‘dispose of’) something (an ‘asset’) that’s increased in value.
It’s the gain you make that’s taxed, not the amount of money you receive.
However, if that gain is made within an ISA wrapper (or under some other circumstances), no CGT is payable. Once that "disposal" has happened (whether or not it attracted CGT), that is the end of the matter as far as tax is concerned.
If you chose to take the money out of your ISA, then that in itself won't cause a tax liability. However, once out of the ISA you will have lost its tax-free protection, so anything new you do with the money might – at some later date – attract tax (for example, capital gains tax, or tax on interest). For this reason, if you were selling the original shares to reinvest within the ISA, you may need to make sure that your ISA provider understands this and doesn't treat it as a withdrawal.
1 Obviously, if you later do something else with the money that does attract tax, you will have to pay.