Re: Lack of a secret ballot is a greater problem
Yes the numbers are there for auditing purposes - if required.
Yes they're covered over before the paper is handed out.
This is why ballot papers are destroyed shortly after counting if there is no challenge
The very few cases of personation and multiple voting that have taken place in the UK in recent history (as in, the last 100 years) made no difference to results in any case as they did not happen in marginal seats.
In marginal seats or where things are tight in results, _every_ ballot is carefully counted and recounted a number of times and voters vs rolls are audited to ensure there's no suggestion of hanky panky going on.
There are enough checks and balances in the system that the far bigger risk (and the elephant in the room) is not voter fraud, but count manipulation - do NOT let electronic voting or counting take place, it's just too risky.