The Peggy cage is far too small for a Syrian, although appreciate it was the only cage you could take home that day. I would suggest the Alaska cage from Zooplus. It's about the same size as the Hamster Heaven (a few centimetres less deep and a few cm wider) plus it's a little bit taller so easy to fit an 11" or 12" wheel in. It also has a nice big front opening door. Not as glamorous but it does fold flat for storage and you can make it look good with toys
And it's only about £34.
Alaska Hamster Cage | Free P&P on orders £29+ at zooplus!
Or if you can go a bit bigger, the Barney cage has narrow 7mm bar spacing. There is no way your hammy could get out of that - providing it's a syrian and providing the top roof door fits properly (if not you could put a book on it or something). The gaps at the corners and front door tops are slightly bigger - near 1cm - which is fine for a Syrian but if you have a dwarf hamster you would need to cable tie those together a bit. The barney is £49.99 and comes with a good sized house a good platform and a basic 8" wheel which would be a good starter wheel.
Barney Pet Cage | Great deals at zooplus!
The Hamster Heaven is a lovely cage but most people end up removing the tubes and penthouse (also escape routes, plus hammies can block up the tubes or get stuck in them) - and then you have - a bare empty cage. Which is more or less what the Alaska and Barney and Savic Ruffy are
From there you add lots of substrate, your own toys, a good sized house for them to nest in (cardboard tubes and tunnels are better and replaceable) and you can also make toys or use tissue boxes etc. For the difference in price between those and the HH you'd have some money left to buy a few toys anyway.
Our Syrian had the Barney cage - it's great! I can highly recommend that. I wanted 7mm bar spacing to stop mice getting in. When we had a mouse problem I was worried about that. Although the Barney costs about £15 more than the Alaska it comes with a really good house (you would need to buy a house for the Alaska as the white one on the shelf is no good for a Syrian - the holes are a bit too small plus a house needs to be open underneath and sat directly on the substrate so they can bury hoards and burrow down and get cosy and make a big nest). And a wheel big enough for a Syrian for starters. In other words - it is ready to go - you just need plenty of substrate, toilet paper strips for nesting, a few toys, food bowl and water bottle.
I think the cages are better than the tank style for a very active Syrian (yours sounds to be!) because there is more scope for levels and you can use the additional height this way.
The Alaska and Barney are both from Zooplus and it can take a week for them to arrive - sometimes it's only 2 or 3 days - depends what day of the week you order sometimes. If you order the 28cm wheel at the same time, you don't pay postage on the wheel.
Small Pet Exercise Wheel | Free P&P on orders £29+ at zooplus!
Then you can take the Peggy back to Pets at Home for a refund
You'd need to do something fairly quickly as you won't be able to fit much more than a wheel in the Peggy.
The other thing I like about the 7mm bar spacing is the substrate doesn't fall out
This was our Syrian's Barney set up, to give an idea