Ok, work the numbers.
You bought for £250,000 and it's now worth £430,000 - that's £180,000 increase. Surely you paid more than £20,000 over the last ten years (including your initial deposit) towards the equity of the property? You should have significantly more than £200,000 in equity.
You want to spend £100,000 on an extension - presumably you'll get an extra bedroom for that but potentially not given that you've not mentioned the upstairs in your OP and (frankly) building prices are mad right now. So, if 3 bedroom properties are selling for £500,000 in your area then you've spent £144,000 (when you factor in the interest on the loan) on an extension that only increased your property value by £70,000. Spending £144,000 to get £70,000 is patently a terrible idea.
If you can afford to pay £1800 to a lender and you have (probably in excess of) £200,000 equity, why can't you afford to move to a £500,000 3-bedroom property? On a standard 4.5x multiplier, you'd need an annual income of just below £67,000 (plus enough for stamp duty and fees etc) but it should definitely be feasible. If your income is less than that then, frankly, you absolutely should not be repaying £1800 to your lender. If you cannot afford to move then you cannot afford to extend.
Flatly, the numbers do not add up to anywhere near a sensible decision. You'd be throwing away thousands and thousands of pounds, not to mention the risk that you default on the payments if cost of living gets too much or something impacts either of your incomes. Plenty of people are commenting that they did it but that's entirely irrelevant - they aren't you, they aren't living in your house, they don't have your income. It's a bit like asking "should I lose 10kg" and overweight people might say "I lost 10kg and I feel way better" but if you're significantly underweight then losing 10kg is an awful idea. Based on what you've said here, you absolutely should not do this.