Gas Oven Problem

Change the thermocouple

The probe of which you speak is almost certainly a vapour pressure safety device. If the pilot burner is heating it correctly then it is probably knackered. If you follow the "wire",it should lead to a valve. The whole vavle assembly incorporating the "wire" and probe come as one. DO NOT let anyone disable this item to get the oven to work as that would be an offence under the GSIURegs in that it is a safety device.

Whilst it is true that many ovens (and grills) made more recently have a thermionic valve mechanism for flame failure detection I don't think it's true here. The OP says it lights and STAYS on the pilot. I think therefore it is more likely that the flame failure device is a liquid expansion valve type device.

Repair would be by replacement of the entire oven gas valve which will include the capillary and the probe end (broken) so it's a fairly involved piece of work.

The OP should ask the Landlord when someone is going to arrive. If that gives no joy then they should send a letter by registered post to the Landlord. If no one arrives by the due date (7 or 14 days from posting IIRC) then they can get their own fitter in to make the repairs (unless the parts in unavailable in which case you buy a new cooker or comparable quality). The payment can then legally be withheld from the rent, but the Landlord MUST be given a fair opportunity to make repairs first.

He seems to already have had that but you need to give it formally.