Even if there were increases they would only be marginal in the overall scheme of things taking into account the cost of a weekend break to a European city and given the wanderlust of your average Brit an extra couple of quid per person, per flight isn't going to dissuade many travellers in booking their leisure trip with Ryanair, or anyone else. That is why APD is such an easy tax to levy, rather as IPT (for insurances) is.
The Ryanair rant probably has more to do with aircraft shortages and convenient excuse to cull marginal routes as others have intimated and I fully expect to see blazes of publicity from Ryanair when they "create xx jobs" and "add £xx to the local economy" when new routes are announced from UK. We had similar toothless threats when the UK finally exited the EU.