A few points I guess.
It IS a co-incidence that the sensor failed at the time the oil filter was being changed. but I very much doubt you can determine / prove anything either way.
If the crank sensor you had on the car lasted 7 years, then it has done bl**dy well!
I strongly suspect that after that much time it was fragile anyway, and maybe when the filter was changed the cable got distrubed, and finished it off.
Even if you were to get the old part back, and find a bit of damage - you'd have no way of proving the oil changer did it.
I personally think you have no recourse at all, against the garage. Just put it down as a learning experience.
I don't mean to piddle on your bonfire, but I must tell you for your future benefit - £140 for a crank sensor is obscenely high

On Trade club (which you personally can get via Autobahnstormers) a new crank sensor is £35 from memory, and no more than 15 minutes to make a good job of fitting it.
Have you considered doing a bit of DIY servicing and repairs? This would save you the worries of visiting ham handed-mechanics, and anyone able bodied can do it. Most common jobs here have a guide, including fault code reading, crank sensor replacement, and oil and filter change. Plenty of advice in the help section, and in the worst case, some members in Derby near you
