The guidance here BIM37620 - Wholly and exclusively: duality of, or non-trade, purpose: travel costs: to and between sites
advises where an 'itinerant' trader's base of operations is at their main residence, the cost of travel between residence and the sites at which the trader works, should be allowed.
The regular travel to a client's place of work, could be considered your place of work and the travel costs would not be allowable
You will need to make a decision based on the guidance here -
BIM37635 - Wholly and exclusively: duality of, or non-trade, purpose: travel costs: home to work: predictability of places of work
whether this particular travel is allowable or not.