WiFi Router unresponsive

I'm looking for some advice from people who know a bit about wireless router hardware.

I help run a small but busy pub in the highlands. We have a standard TP-Link wifi router which we currently allow free access to for customers. In the winter, when the pub is quiet, we have no problems with the router at all. However, when it gets very busy, devices struggle to connect to the router.

I'm uncertain as to whether the sheer volume of traffic is just slowing our internet connection down to a halt, or if it's a matter that the router just wasn't built to deal with the kind of volume that it's getting. My instincts tell me that it's probably the latter since it's the router that devices are having trouble connecting to.

Would you concur with that assessment? If so, are there higher capacity routers that might do the job better? Or would we be better moving towards a pay-per-use model to slow down use of the router?

Thanks a lot.