To expand slightly on carrdelling's answer...
(For the moment, I'll assume your original £100,000 was invested in a single "thing": e.g. the shares of one company or a single mutual fund etc.).
If, after a year, your investment has doubled in value and you sell £24,600 worth of that "thing" then you will not pay any Capital Gains Tax. The original value would have been £12,300, so you've made a Capital Gain of £12,300. Because this exactly matches your allowance, no tax would be due.
Of course, if you were to sell any more in the same financial year, because you have now "used up" you tax-free allowance, you will pay CGT on the total gain. Note also that the gain is unlikely to remain 50% of what you sell for... the gain is the difference between the price when you bought the "thing" and the price when you sell.
If your original investment was not a "single thing" (and the general advice is you shouldn't put "all your eggs in one basket"), then things will usually be a little more complicated.
With a "basket" of 10 different shares, even if collectively they have doubled in value, it would be very unlikely that all 10 shares have exactly doubled in value. Some may have risen by 120% (more than doubled), some may "only" have risen 50% and some may have fallen to 80% of their original value.
For each type of share you need to determine the value when you sold it, and the value when you originally bought it. The difference between the two is the capital gain (or loss). Add together the gains/losses for each share you sell, and that total will be your total capital gain.