The Ordnance Survey have Landform Profile and Landform Panorama that were based on their contour data, but it is not fantastic quality, and it is based on very old data. But it is now free to download, so if you just need a dataset to play with, it's a good choice.
I've used GetMapping's NEXTMap Britain 2 lidar data, and it is of generally very good quality, providing both a "treetops" dataset, and a "bare earth" dataset. But the tiles are very expensive once you start getting reasonably-sized areas. It has a horizontal resolution of 5m (I think there is a cheaper 10m resolution dataset), and a good vertical resolution (about 20cm IIRC).
The Environment Agency has released its LiDAR data on an open source license. It covers about 72% of England and Wales: https://environmentagency.blog.gov.uk/2015/06/16/free-mapping-data-will-elevate-flood-risk-knowledge/