There's some useful guidance here http://www.hse.gov.uk/pubns/indg382.pdf and, although intended for HGV drivers, more  here https://www.gov.uk/drivers-hours/gb-domestic-rules

From your post the majority seem happy to comply with existing company arrangements (Tues - Thur site work / Mon & Fri travel days).

Unfortunately as with any arrangement they do/will not fit everyones personal wishes and circumstances.

By paying overtime for travel on the Thursday evening your business is condoning the behaviour (and possibly making the situation worse as others could then claim custom & practice should they also wish to minimise time away from home - "well I can set off Tuesday morning at 03:00 Hrs")

You mention they come to work Friday morning at 08:30 - as this is a reluctant traveller is there more local work they could be transferred to or a region with lower travel times?

The job description should clearly specify what is expected of the employee and what the company expects in return - is it safe to presume they were fully aware of this before taking the position?

Elf "n" Safety (working hours) is possibly being used as a scapegoat to bring an unmanaged situation back in to control. Have a chat with the engineers line manager and see what their thoughts on this matter are.

I had to manage a similar scenario one. We had people doing bat surveys (not the ones you play with but those that flit about at night) and their managers decided that they should put   in a full day in the office then drive out (to sites across northern England and Scotland) as the bats only come out at night. Then drive back to base to drop off their vehicles. They could then take the rest of the morning off, be back in the office after lunch. So they were doing loads of driving on top of doing a full day at work. They were not allowed to stop out overnight and use a hotel/B+B as this was not included in the project budget.

We had to puta stop to this and get the managers to realise that driving back to and from the bat viewing sites was part and parcel of the working day and their staff were working excess hours.  If someone had and accident it would have serious implication beyond the merely legal.

 And yes Chris is right some government agencies have a strict 12 hour rule.

That the person is doing 12-15hrs pretty much from hotel room to house door is not overly spectacular providing it is occasional. suggesting they started work 8am on Thursday and ended 15 hrs later ( 11pm), or there about to be off work for about 9hrs to then be into work for 8.30 the next morning again is not a wow factor, but something to be managed and monitored.  What the driver is doing is more hours than the others, when they are trvaelling on Thurs evening whilst the others are resting in their hotel and is also working Fri morning when the others are driving.   Do you have a policyt that says the minimum break between end of work (including work driving) and the next period of work (including driving for work). Out of interest, inclusive of driving, what is the typical working day for the team on tues/wed/thurs?   There are options where you could 'demand' the worker does not drive on thurs, adjust his work on thurs morning to reduce his overall working day, extend the friday start to ensure 11hrs rest (Probably the most balanced response) and other permutations.   Does the company spcify the MAXIMUM working day, inclusive of driving, if not, this slightly extended day and arranging a late start on friday could be easily managed. As above, the Drivers Hours Regs set out minimum of 9/10 hrs rest or max 9/10hrs driving which wraps within a max daily work of 15hrs per 24hrs.  Whilst this is not directly applicable to your engineers, its a fairly goos base line - but also consider the other restrictions that go with these regs on rest etc.   Driving and rest is always a bit of a challenge, when legislation empowers commercial drivers to drive non-stip for 4 1/2 hrs without rest whilst other sources such as RoSPA recommend a 15-10 min beark after 2 hrs!