I have the same thing, no lunch allowance when working on another site that belongs to the company, we get £5 if working on a client site or elsewhere. I work in London a lot, there is a subsidised canteen where I am, but the canteen can’t/won’t cater for my dietary needs (coeliac) so I have no choice but to go to the more expensive shops, and work won’t cover it.
I bring lunch from home if I’m just down for the day, but can’t do that if I’m staying overnight. If I am staying in a hotel with a fridge in the room, it’s easier, but not all places have that facility.
You could get a hotel with breakfast included, and then buy your lunch in the morning and use the breakfast allowance….