A lot of website companies around here will rent you one. You pay every month, and the day you stop paying, the site goes off. You never owned it. Some of them will not even hand over the files.
We do it the other way round. You pay for the build, the site is yours: the design, the content, the code, the domain. Host it with us or host it anywhere you like. If you ever leave, you take it with you and we help you move it.
Paying monthly is for website builds and redesigns. If the full price is too much in one go, a £200 deposit starts the build and comes off the price, and the rest is spread over 6, 9 or 12 months with no interest, under a written contract. Until the last payment is made, the site runs under that contract, and a payment more than a week late switches it off until it is paid. That is still not renting. The deposit and the payments add up to the same price, the payments end, and then the site is yours outright.
The monthly care plan is optional, though we do recommend it, and plenty of clients take the build and host it themselves. See what everything costs