The Alexander is very suitable! I'd say, if you can't get a detolf, get a 100cm cage. Zooplus has a very good choice of reasonably priced Syrian cages, and as Racing Hamster says - if you show your Mum the reviews on the web page and show what a reasonable price it is she may well be swayed. The Barney is also a 100cm cage and I think it would be easier to set up than an Alexander as it is a bit lower, but still high enough for the shelf it comes with. I think the set up of the Alexander could be limited due to the shape of it and the platforms it comes with and the big drop in the gap between the platforms. You can work round that, but the Barney is only 6cm lower and an easier shape to work with. It is also less than £50!
Out of 100cm cages there isn't a huge choice other than the Barney and Alexander, under £100. At £139 though there is the Living World Eco Habitat which might be the next best thing to a detolf! Although I reckon the lid still needs meshing as it has 2cm slots in it and if you put deep bedding in (which it needs really) a hammy would probably get up to the top somehow.
Living World Green Eco Habitat | Free P&P on orders £29+ at zooplus!
The Falco is an amazing 100cm cage - part glass tank and part cage top but it is expensive at £169. It also needs a bit of working out to set up to avoid drops (although you can fill the base with bedding so your hammy can do some tunneling) and access is just through the top - but then access is through the top with most tanks.
I was really wanting one of these for a while and worked out a few set ups on paper and decided the best set up for it was with 45cm depth of substrate (5cm below the top of the glass tank) and no shelves and just use the top part as you would a regular cage, as the main reason for a cage like that is to give very deep bedding.
Hamster Cages: great selection at zooplus: Small Pet Cage Falco
Another tank style cage, within budget is the Maxi Duna Multy - it's the same size as the 100cm Zoozone but doesn't need meshing as the bar spacing on top is less than 1cm. You can fit a 29cm wheel in there.
Cage Maxi Duna Multy
The Mamble is also a 100cm cage - it's a rat cage and quite high so could do with a full level in it for safety really, but it is cheap compared to a lot of cages at about £40 - I've heard it's a bit difficult to put together.
http://www.amazon.co.uk/LITTLE-FRIEN...ds=Mamble+cage
The Alaska, Hamster Heaven and Savic Sky are all good cages, but are 80cm cages and having an 80cm cage myself it just makes me want something bigger all the time! So I reckon go for at least 100cm cage.
You might want to drop the odd little 'fact' to your Mum that you have found out which could help get what you want as well. Like Hamsters do like climbing but they aren't very good at getting down and can break bones when they fall from the top if the cage if they fall on something hard. Also that recent research shows that deeper bedding lowers a Hamster's stress levels as they can dig tunnels, which is what they do in the wild and are kind of programmed to do. A detolf would be perfect for this - you could have a section with very deep bedding and still plenty of floorspace. It does need a lid making though and that means diy.
I think if I was starting looking for a cage from scratch now, under £100 I would get the Barney. I like the Maxi Duna as well but the wheel can't be raised in there due to the height limit. In the Barney a Hamster could be very happy with lots of floor space, a shelf level, space for a big wheel and enough height to either hang a Wodent wheel from the roof (increases the amount of floor space for digging basically) or stand a wheel on a platform so the hamster can have a hide under it. It's also like a blank canvas for setting up in various different ways.
The Zooplus cages are only available online really but you can tell your Mum that they have very good customer service and will replace anything that arrives damaged.
I think the Barney cage could be a good compromise between what you want and what they think a Hamster needs lol. It has good floor space and a shelf to climb on - you can hang a sputnik and a grass hammock in it maybe - and you if you wanted to do some sneaky diy you could put some pieces of plexiglass inside the bars at one end and have a digging end with deep substrate (I've been working this one out on paper too!). My current solution for the far end is - have the base full with substrate and have a 15cm high long cork tunnel on top of the substrate at the far and and kind of mound the substrate sloping up to the top of the cork tunnel with a bit of plexi front and back to stop it spilling out, so the cork tunnel is a kind of bar barrier at the back and the plexi at the two sides up to the first door.
Sorry I'm getting carried away there!
Re: Any suitable good cages in uk?
and now it's set up my mum agrees that it's a great size for the money. I had a hamster heaven before which is the same as a sky metro and I like it a lot though I felt my big, very active syrian needed something a bit bigger, it's still a great cage. It's really the only suitable once that pets at home sell, except maybe the Ferplast Mary rat cages but they would need a bit of DIY meshing as the bar spacing is too large. I hope you get a decent retail assistant in p@h who isn't just wanting to make a sale and gives you good advice! 
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