Flying well above 1000ft, say 3000ft, reduces the probability more than anything else - by at least an order of magnitude. So much so that there have been no UK midairs (TMK) above 2000ft - ever.
While I agree with you, and when I can I always fly above 5000' (6.5-9.5k is a good altitude), many places in the UK you can't. For example along the Solent everyone is squashed to below 2000' unless you manage to get a clearance from Solent to go higher. Invariable everyone then decides to fly at 1700-1900' in any direction!! Scary stuff, and I sometimes wonder whether you'd actually be safer flying at sub 1000' (say 800') in these areas or ask Solent if you can fly at 2100' (or higher if they will clear you - I reckon a 2100' clearance should be no problem). Perhaps there should be advisory altitudes "Aircraft heading west do so at 1500', aircraft heading east fly at 2000'"? You are unlikely to find many other aircraft that low, most going into Bournemouth will be at 1700-1900 too.