Firstly are you saying non bridal as in style or colour?
Because it's entirely possible to get "wedding dresses" that aren't traditionally bridal in either.
If you mean a toned down version maybe look at bridesmaid dresses which tend to be less "meringuey" and come in a huge variety of colours.
The vast majority of bridal retailers make to order so plus size and tall not a problem at all, though I'd say you're not that big actually, I've dressed up to size 40 and most retailers usually go up to a 34-36 as standard. I'm an 18 myself and so I understand about wanting to play down certain areas of your body, but please remember this:
*Your fiancé loves YOU they're marrying YOU - as you are, as you look now. They think you're beautiful and I bet you are too. Maybe focus on the parts you do like? Maybe you have an hourglass shape? A fabulous décolletage? A pert bum? And play those UP!
My belly is the bit I hate most closely followed by the bingo wings! But I have good legs and a very full and pert bust! So when I'm dressing for an occasion I focus on presenting those areas well with downplaying the worse parts secondary.
What sort of colours do you like?
I used to work in the industry and the other advantage to buying bespoke is you can have it altered to your specifications. So eg if you like most of a dress, but it's strapless, it can be made to include straps or sleeves (depending on specific style) or you can have a cape/bolero/stole made in perfectly matching fabric and decorations to go over the strapless dress to cover your arms.
Several friends and clients of mine have done this for a variety of reasons including to cover a tattoo that was a bit risqué!
Styles are much more varied now.
Have you actually tried anything on yet?
The thing with ball gowns/evening dresses is they're not something we wear regularly now so we don't tend to know what actually suits us until we try a few on.
How tall are you? Most are made (even if intended as samples) to fit around 5'10" simply as that's probably as tall as most women get to and it's obviously easier to take a hem up.
I've had many instances of a bride being set against a particular style or colour I've proposed and then they try it on and love it! But that's of course when I've seen them in person - I highly recommend you go to a proper boutique.
Just from a brief look at current offerings these are plus size and quite a few have proper covering sleeves
www.truebride.co.uk/1564/True-Curves
I love the colour of this and the sleeves might be the sort of thing you're looking for ?
www.truebride.co.uk/2229/Hope-M457
This is a little prettier though?
www.truebride.co.uk/2139/Fearne-M440
I do like the sleeves here
www.truebride.co.uk/2146/Fliss-M448
Personally I find wrap styles are generally very flattering I wear wrap dresses a lot
kelseyrose.co.uk/product/17515-metallic-wrap-dress/
Hope that helps get you started I'll keep looking