Fixed Penalty Notices (FPNs) do not carry any sort of custodial sentence. If Johnson did not pay them he would end up in the local Magistrates court. Since breaking lockdown restrictions did not carry any custodial sentences (I think the maximum fine was £10,000), all that could happen would be that the fine increased or he received a community service order; and he would get a criminal record.
According to untrustworthy mainstream media and even less trustworthy Twitter, he is probably going to end up with three FPNs, one of which has already been served. I am sure that he can find the money down the back of the Russian-bought sofa at No 10 to just pay them.