Okay so I'm a hairdresser, not a Barber. I work in a salon and do like 90% women. I'm also in the UK. but, here's my thoughts.
Firstly tips are already huge in the industry dude. However, deciding whether the tip is kinda 'necessary' or something you should feel guilty about not doing is a bit tricky for a client in my opinion.. most hair stylists rent the chair or work on commission and depending on the level and type of salon the tips can either be a massive deal or not really a concern. I'd wager that barbers being so competitive and setting usually lower prices than salons, the tips are a big deal to a lot, but even that's not totally true with the rise of the upmarket Barber Shop in the past 10 years. There's a huge disparity between min/max wages in hair styling. On one hand you've got low earners that are typically recently qualified, on the next you've got people pulling in £50-60k+ a year without breaking a sweat.
If your Barber is working in a decent place I think they won't really care about tips. But you'll also probably be paying more for the cut anyway. I shouldn't generalise but.. The stylists working in upmarket places often won't care about tips, those places will give them opportunities outside the shop in fashion and editorial work which is probably the whole reason they are there and they'll also be earning a decent wedge without tips. That's not to say there isn't talent or passion in the £10 shop, but in general I think you'll find a different approach in those places, where it's much more about just cutting hair as a job for a lot of people. The whole thing is basic in the sense its no fuss service and a good standard cut, but tips are often integral to their income as there is no hourly wage and prices are low to compete. After that its all about volume and the tips add up.
Having said all that, the misconception that hair stylists don't earn much money is severely out dated in our shiny, modern service based culture. Honestly Ive felt guilty at times to recieve a tip.
Anyway, do what you want about tips, I'd give everyone exactly the same service and level of professionalism regardless and if you suspect that they wouldn't be doing the same, then why are you trusting this person with your hair in the first place?