I don't know how recession will affect FTOs but generally UK universities and training establishments do well in times of recession. The reason is that people naturally revert to gaining education or "retraining" in harder times.
Learning to flymay be different. There are many many motives for learning, I guess, from those who just want bragging rights or those who crave an airline job.
The dynamic of the industry maybe set to change depending on socio-economic stuff.
For example, really rich people are usually unaffected by recession - so the potential
fly the chopper to the party guys will still want to learn. But the young wannabe commercial pilot may find parents less able to pay for their training unless they are wealthy. The UK is set for an unpredictable few years.
Nothing in aviation is certain at the best of times.
The only certainty in aviation is the CAA charge to rubber stamp an A6 piece of paper
The global demand for FIs is expanding, however. Offering good pay and a great experience for the adventurous FI, countries like India offer fantastic opportunities.