According to Churchill’s History of WW2, on July 10, Fighter Command had a total of 54 front-line squadrons operational, with 656 aircraft available. He doesn’t give figures of squadrons for earlier, but did say that at all time, 450 front-line fighters had been kept in Britain during the Battle for France, with their pilots having been kept from the Battle of France.
Egbert Keiser, Operation Sealion, states that at the Fall of France, 11 Group had 196 aircraft operational, but doesn’t specify how many operational fighters were in the other 3 Groups. Typically, 11 Group had around 50% of operational fighters, so a rough rule of thumb would suggest around 400 operational fighters in Britain at the Fall of France.
Liddell Hart, History of the Second World War, states that at the start of July, there were 400-500 front-line fighters in the south of England.
The discrepancies seems to be that Churchill’s figures include all fighters, while Liddell Hart is only counting Hurricanes and Spitfires. Keiser’s figures, because he focuses on the German side of things, is based on Luftwaffe estimates.
According to the RAF website, at the start of July 1940, the RAF had a total of 1259 trained pilots. Irritatingly, it doesn’t specify what proportion were fighter pilots, but an assumption of 40% gives us just over 500 pilots, which is not out of line with the numbers of available aircraft.
According to Christos Turner, on 2 July, the RAF had an available strength of 525 Spitfires and Hurricanes.