At the moment, to my knowledge, there is no complete LIDAR DTM or DSM for the UK that is open data. I have been looking for years.
The open LIDAR that is available is open because it was flown by the Environment Agency to carry out flood risk analysis. Therefore the coverage is limited to river catchments, coastal areas and low lying flood plains.
Here is a link to a catalogue of the LIDAR data on data.gov.uk by Chris Guitteridge https://github.com/cgutteridge/uklidar
Here is a good summary, it's a bit dated as it is Oct 2015, but it is a good read. Collecting LIDAR data is expensive so complete coverage is unlikely to be open data anytime soon.