IF (big if) we ever leave the EU, will the cost of servicing a Peugeot increase significantly?

Most pathetic question ever.

The labour cost probably won't change, but the parts cost may increase by 10% if we leave without a deal, as the WTO tariff on cars and car parts is 10%.

Short answer: No

Long Answer: Why should it? Labour costs will be the same, sundries such as oil and filters are mainly universal but may go up (or down) depending on tariffs and exchange rate fluctuations.

Depends on what kind of tariffs you negotiate with the countries that make parts for Peugeot. I doubt many of the parts actually come out of the EU.

If you Brits still don't know what the effects of not being dominated by Germany will be it's no wonder there is so much confusion in your Country. I highly recommend securing your borders and blocking anymore Muslim invaders!

Depends on what tariffs, if any, the EU imposes on automotive parts shipped to Britain.

don't know, but I bet it will for a BMW! LOL!