Great Britain, indeed had a Navy. But in my perception, this navy has been in decline, at the begging of ww2. It was not the navy the kept the empire in previous 200 years.
As after ww1, All major world powers have started reducing military budgets, and decommissioning of heavy equipment (artilleries, navies, airplanes, etc) never expecting war on world wide scale, and certainly not in Europe.
Britain was not exemption.
I remember Winston Chushill notes from his memoirs, when taking position of PM, and first sea lord, before that having problem of recommissioning some heavy pieces of artillery from military ware houses, left since ww1.
navy had its problems.
Not sufficient number of destroyers,for duty of convoy escorts. Old fleet, on another hand.
They signed a deal with US to get urgently Escort destroyers, for exchange for military basis. It was so called destroyers for bases deal. This improved Great Britain naval capability in ww2. And helped them to survive, because convoy were bringing vital supplies and resources for war effort, plus food.
I think that in that time, naval doctrine was still heavily influenced by the doctrine of large vessels - battle ships, and aircraft carriers time was yet to come. Air craft carriers have not been proven as backbone of modern navy fleet -yet. Only few in service, and battle ships,. cruisers, heavy cruisers prevailed, with many of them obsolete since ww1, that survived first wave of scrapping during previous budget cuts.
UK paid the price, by losses in tonnage and human lives.
HMS Hood sunk by german battleship Bismarck, 1941
HMS Royal Oak, sunk on anchorage in well protected Scapa flow base, by german sub... u47, 1941
HMS Repulse, sunk in south china sea, 1941
HMS Prince of Wales, sunk in south chine sea, 1941
HMS Glorius, carrier, sunk in 1940
HMS ark royal, carrier, sunk 1941
Those are capital ship lost, only by 1941 - how much was left then to keep fighting the next day?
etc... There might be few more, but they were sunk either by modern ships like Bismarck, or by airplanes or subs, as modern technology.
After the European ground has been lost to Germany in begging of ww2 with occupied Poland and France, and before invasion of Russia, great Britain was the only country fighting Germans, and really loosing their ground, with culmination at Dunqirk.
And even before that royal navy realized they need to upgrade their fleet - FAST. In such environment, in 1940, they signed the deal with US for escort carriers, in return to give to US the bases.
The only other part, of occupied Europe that kept fighting, at that time - and till the end of war were Yugosalv partisans, which at all times kept at least a part of liberated territory, till end of ww2... Which in advanced stages of war gave allied pilots a chance to land, or parachute when flying to and from bombing missions across the Europe. In other parts of europe, they had best chance to get KIA or POW... no free territory to land...if they plane was shot.
But that is another story. However, this is less known fact.
Bottom line: UK - Navy they had, but US helped greatly!