Local Solicitors will give a quote, usually. And many would welcome the work theses days, so you're likely to get competitive prices.
BUT. You pay for what you get. Conveyancing isn't a "tick-box" exercise and you will want to have a good job done on the conveyance. Some conveyances can be complex (for example, if there are planning issues, right or way issues e.g. the neighbour's sewage pipe coming in through the property without a formal wayleave) etc.
Conveyancing (if you're buying) will involve the Solicitor investigating the title and advising on any pitfalls or issues with the property you're buying. You'll want to acquire good marketable title to any such property, such that you can sell it down the line without any issues. If you're selling, the same issues can arise except you're the one trying to convince the purchaser to buy.
A huge problem during the last boom was so-called "conveyer-belt conveyancing" which saw some Solicitors charging unnaturally low prices, and getting a high volume of work, only for such work to end up being badly done. In many instances, the title problems only surfaced years later when the buyer ended up wanting to sell.