While an ISP might offer free space, I'd say it depends a bit on what one wants to use the web site 'for'.
I've seen people spend years working on their website, getting more and more visitors and then find
a) that search engines all know about the ISP-based webspace (eg youruser.plus.com/ if user was on Plus.Net) and
b) the ISP has a limit on how much web traffic is allowed (in the case of Plus.Net it was 250 MB in a day)
the consequence is that when the site is very popular, the ISP might have a policy that "suspends" it for excess traffic (admittedly an ISP might be protecting itself - if someone put up 200 MB of MP3 music tracks and then told every one of their friends "oh yes, new album is online at username.plus.com/music" then the traffic load could go through the roof.
However, suspending the site might mean the user wants to get hosting elsewhere, and then all the search engines will not be pointing to the correct pages, so they lose visitors.
Use ISP space for testing the website, perhaps, but I'd recommend registering a domain name (.co.uk and/or .com or .org.uk / .org if it is non-commercial) and getting hosting from some other company (not the domain registration firm) so if you get into a dispute, you can switch to some other web host easily (via changes to the registration firm).
If you are planning to use it for business, then one firm I've used is Hostroute.co.uk and another is HeartInternet.co.uk.
Hostroute offers a widely used "standard" control panel called "cPanel" which allows the user to set up POP mailboxes (and/or mail forwarding into a Google /Hotmail/ other mail service), gives usage statistics showing graphs of how many visitors per month and per day, etc, and offers plenty of other features.
Heart Internet has its own control panel, and offers similar features (free hosting if the web traffic is below 100 MB a month, for a domain registered with them, so you can start off free, and then when visitor numbers increase, you would need to rent hosting from someone - eg Hostroute)
If you're just getting started and it's not intended for business, more as a hobby site, consider looking on Ebay. You can find some bargains - in the past I've put websites up on hosting costing US$ 10 for a year - averaged out this is about the same as you'd spend on a (small) bar of chocolate each month! OK, small risk of "pay peanuts" syndrome, which someone will no doubt warn you against, but it's not costing much and allows the chance to try out different control panels.
I've used a number of different control panels now - LXAdmin, DirectAdmin, Ensim, Plesk, and cPanel... (plus a few from different companies which have built their own control panels).
Can recommend cPanel as it is perhaps the easiest yet gives lots of extra features if you/DH want to explore them.