Hi, welcome to the forum

Can I ask you to type your postcode in here
https://www.yorkshirewater.com/water-quality/check-your-water-hardness/ and tell us what the number they give is, please. The unit should be "mg/l calcium".
I know someone who used to live in York and they said the water was quite hard.
I should explain that water hardness is another thing we've come to understand better in more recent years. Fish need to be kept in water similar to that in which they originate, and this is more important for wild caught fish. Hardness is the amount of mainly calcium, some magnesium and trace amounts of other metals in the water.
Fish from soft water which are kept in hard water will not live out their full life span. Soft water fish have evolved to retain as much calcium as possible from the water, and if there is a lot of calcium they retain too much. Autopsies of cardinal tetras kept in hard water show calcium deposits in their organs which shortened their lives.
Fish from hard water suffer if kept in soft water. Hard water fish have bodies which have evolved to excrete all that extra calcium which is in the water they ingest. In soft water, they continue excreting calcium but there is not enough left for their bodies to perform properly so they become sick much more easily.
Unfortunately, both the fish you name - green neons and cories - are soft water fish, which is why we need to know how hard your water is. And wild caught fish such as green neons are more likely to suffer if kept in a hardness that is "wrong" for them.
If it does turn out to be hard, there are many fish you can keep, from livebearers such as guppies and endlers (the others get too big for your tank) through to fish such as some of the Pseudomugil species.
It is possible to 'soften' water by mixing tap water with 'pure' water such as reverse osmosis (RO) but this is not something to undertake lightly. If you really do want soft water fish, we can talk you through this.
Is your local MA the one in Poppleton? I live in Teesside and we use the Poppleton park & ride when we visit York - so naturally I go into the garden centre to look at fish

MA is one of the better shops, but some branches are better than others. Be careful about taking advice from any shop worker, even those in MA. They stock soft water fish because they are not there long, and they don't care what happens after they leave the shop.