If you're going to be hands-on and have skills and free time then an extension could be a great idea.
If you're going to sit on a chair while paying someone else to do everything then these days you'd probably pay less just to buy a bigger house. This is because materials, labour are much more expensive than they used to be.
Plus most "builders" don't pick up a hammer these days, they stand about and make phone calls now and then. Pay someone £300 to dig a hole then charge you £3000 for it.
If you don't want to get your hands dirty but have technical skills then you can save a lot by designing and/or managing yourself, and employing tradespeople directly, cutting out the middleman.
Extensions routinely cost more than £100,000 these days, for something fairly unremarkable, if you want to be like the people on telly and do nothing but choose the curtains and carpets.