Having gone through the IVF process twice, once on the NHS and once privately, I can confirm that the private clinics use the same screw top lids. The private clinic doesn't expect you to use the disabled toilet and does provide jazz mags however.
The private clinic I went to had a room that clearly used to be a toilet, with a chaise lounge where the pan used to be, frosted glass window right next to the car park and a code on the wall for the WiFi, that didn't work.
The NHS doesn't have masturbation cups, they have masturbation pots with a screw=top lid. So you don't waste your precious juices.