Part of the reason freight is slim is the restricted loading gauge, principally due to the tunnels en route. Slightly off-topic, the incline which peaks at Standedge is probably the place where electrification would have greatest benefit including green credentials.
The width of British trains is mainly restricted by platforms. There are some other structures that could (with lots of time and money) be moved further from the track, but setting the platforms back would lead to a dangerous gap for people boarding and alighting. It would need all the trains on a route to be equipped with moveable steps to bridge the gap,
then all platforms to be re-built in new positions, also re-building other parts of the station if the platforms would otherwise be dangerously narrow. There would also be the issue of the tracks being too close together for wider trains - increasing the spacing involves re-building almost everything. All in all it would take decades and cost billions and it just isn't going to happen.
Increasing the height, typically only at the sides where the square tops of containers stick out, isn't always straightforward but it's nothing compared to increasing the width, particularly at platform level. Those routes where the gauge has been suitably enhanced can handle all the standard container widths.
It means we have a different solution from the Continent where all containers fit without loading gauge improvement, but where we have done that work we can handle containers reasonably well. British intermodal wagons could run through to the Continent if they needed to but they usually don't because most containers, being intermodal, are transferred to a ship instead. The only thing that's easy on the Continent and virtually impossible in the UK is carrying road trailers, although again I think the problem is height rather than width.
