The only burger place I remember in Birkenhead was Scooby's, but that would have been early 80's not 70's. Scooby's was (if my memory serves me correctly) on the opposite corner to Roberts bathroom shop.
My then boyfriend (now husband of 27 years) used to think it was the best thing ever going to get a Scooby snack after we'd been to the Pub
, and had never had sweetcorn or tomato relish on a burger before
On the topic of burger joints though I have to mention "What's Cooking". Back in the early 80's that was THE place to go for a meal. You could not leave that place without feeling stuffed to the gills, the food back then was excellent and there was tons of it too. Ahhhh memories