It kind of depends on what exactly you do and how you're set up. If you're a proper VAT number holder, professional liability insurance isn't legally required, but a lot of clients (especially medium-sized companies) ask for it before signing a contract. In your case, since you do web design, a professional liability policy could protect you if, say, a mistake of yours causes damage to a client's website or their online reputation. That said, if you work with small businesses that don't ask for it, technically you could get by without it, even though it's not exactly professional from a business standpoint.
As for prices, they really vary a lot because it depends on how much revenue you declare, how many clients you have, what kind of coverage you choose. I'm not an insurance expert (my world is completely different, with dogs and fires 😅), but from what I hear around, before you decide you should get three or four quotes from different agencies. Don't just go for the cheapest price: check carefully what it covers, the limit (how much they pay if something goes wrong), and whether there are exclusions that apply to you. Some companies offer cheaper plans for people just starting out, maybe with lower limits. Have you tried asking other web consultants or freelancers you know what policy they use and whether they're doing okay with it?