Tyre options for 27 inch bicycle wheels

[Namakwalander]

Hi guys

I have an old road bike that I want to fit a set of slightly wider tyres to. It is the old type road bikes with 27 x 1 1/4 tyres.

Yes, it might be better to replace with a mountain bike, but funds are not allowing for that right now and I would like to be able to ride on some tame gravel roads.

Aparrently one can get 1 x 3/8 tyres (3mm wider), but is that actually possible and affordable?

Thanks

Photo of bike for reference.