Verboten topic aside, there's a difference (for me) between public sex and outdoor sex. I like the sun on my ass when I'm on the job but I'm not particularly fond of getting caught/seen. A few SPs advertise outdoor meets, but not really in London. I would say it's quite risky for the SP for someone she's not met before. A few SPs have been open to some outdoor action but the topic only discussed after a few meets, i.e. after some trust/rapport was established. Had a good fumble in Richmond Park once with a SP.
If you really want public sex, try a streetwalker.