How successful is franchising in the UK?

That would depend on how ‘success’ is defined and as far as I’m aware nobody sets any criteria or creates any measures for franchising as such.
The annual NatWest/British Franchise Association survey regularly publishes good news such as more franchisors, more franchisees and greater total sales than the previous year, and it usually claims that a large majority of franchisees are profitable and are happy with their relationship with their franchisor, although no targets are ever set in advance for what level would be acceptable for any of these items. Even if they were, who would be responsible for achieving them? Compared to many other countries, we could also claim to be successful in that there is no franchising specific law in the UK and there is never likely to be, and even when there are some large-scale business failures of franchised networks they never attract much publicity.
On the other hand, if we were to compare the number of franchisors or franchisees per head of population, the percentage of gross domestic product that goes through franchised outlets or the level of awareness of franchising among the general public then the UK would be a long way behind other English speaking countries such as the USA, Canada, Australia and New Zealand.
So whether franchising is successful depends on your point of view. Generally speaking, I would say that it is, but we have a long way to go before it’s as successful as it could be, by any measure.