Have a look at the first image on this page,
https://www.thompsonsfishrestaurants.com/
It shows what fish chips and mushy peas look like in a restaurant today, the chips and battered fish are deep fried, drained, then placed on the plate and the mushy peas are cooked in a pan on a hob and are served in a small round dish which is placed on the plate seperately.
Some chippies even today use animal fat in the oil, so vegetarians like me need to enquire before ordering.
Traditionally, say late 1940s, fish and chips and mushy peas were one of the first takeaway meals. In those days, very few people had a car and meals were not delivered. Among the shops on the high street, there'd be the fish and chip shop, often called the chippy. They were mainly family run, they were equipped with deep fat fryers for the fish and chips, the mushy peas were cooked in a large pan on an adjacent hob.
For many families, fish and chips and mushy peas, often called a a fish supper, was a weekly treat mostly on a Friday night.
It was traditional not to eat meat on a Friday.
The whole takeaway process in those days was geared around getting the food home whilst keeping it warm and not mixing the contents.
Traditionally, the fish was placed in a greaseproof paper bag, That was laid on more greaseproof paper and the chips were added, and lastly the mushy peas in a paper or card cup with a lid. This was then wrapped ip in lots of layers of newspaper and either carried home by hand which risked oil spill and ink stains on clothing, or placed in a customers bag.
It was commonplace to see hungry people open the packages and eat the contents with a small wooden spatula/fork, dipping the chips into the mushy peas.
Very few chip shops in those days had tables, they were initially a takeaway business. Some owners then realised the profits to be made from customers also eating on the premises and chippies started to provide tables and added extra items to their menus to increase trade.
Thanks for asking about mushy peas, it's brought back a lot of memories from childhood.