Last time I checked the BOE owned nearly 40% of british bonds (gilts). Cost to the tax payer ? Nothing as the coupon payments are simply given straight back to the treasury. The net effect is simply expansion of narrow money into the wider economy through government spending (above taxation) to try and stoke up inflation whilst maintaining asset prices from collapse.
Inflation is a hidden tax. There is definitely a cost to the tax payer here, they can only obfuscate that fact so people don't even know they're being robbed.
True. Though I did say it resulted in expansion of the money supply to stoke up inflation. But in general you are absolutely on the money.