metals4u and steelexpress do a reasonable selection of cut lengths and full bars online. I used to use the local Macready’s steel depot until they changed to new owners who didn’t like cash sales under one tonne. Three changes of ownership later and that site has closed, although the successors have apparently got some space in another industrial estate a couple of miles away.
There was a problem when Tuffnells went into administration, since they were the default (almost only) rapid shipper of longer items in the UK. But they’ve been bought out and are back in business. If you buy full lengths of steel online, they are likely to be the shippers.