Depends what you mean by affordable. And also, you should bear in mind that, where you live, quite a lot of tropical style planting may not survive a harsh winter. We've been lucky this year so far, it's been more like an extended autumn than actual winter.
That said, have a look at Yuccas - these are the hardiest of all the tropical plants, even coming through last winter unscathed here in London, except for Yucca gloriosa, which tends to develop Leaf Spot in a bad winter. The one to look for is Yucca flaccida - there are different varieties of it, but the brightest coloured is Y. flaccida 'Golden Sword'.
There's also Astelia, though that would need a very sheltered, sunny spot out of the wind during winters up there - it made it through the last 2 winters here in London though, despite looking like it had been beaten up by the end of last year's snow. Cordylines, of course, but they will definitely need protection in a bad year.

A lot of retailers sell tropical plants cheap at this time of year - certainly B&Q and Homebase. Have seen Washintonia, Canary Palm, Cordylines, Bamboos etc for a fraction of their summer price. Gunnera manicanta can grow from seed and grows to 6ft in a few years.

Hi, try Fatsia japonica, Monkey puzzle tree (Araucaria araucana), Torbay palm(Cordyline australis) or one of my favorites Brugmansia which I know has withstood recent winters in Devon, but will need some protection in Humberside - alternatively will root easily from even big cuttings (I have rooted 4 ft. branches) and winter indoors.

Fatsia japonica is a must have!

Lobelia cardinalis, hosta's, Pheonex palm, ferns, Passion flowers, Brugmansia, Pulmonaria, Crocosmia Lucifer, Cardoons..

Ophiopogon nigrescens...

Oh yes Bamboo..and Coleus too

And Hedychiums, if you can be bothered.

It's looking quite good already this garden.

;-))

Wow what a response thanks. Looks like some serious shopping and planting come spring. Once again thanks will post some pictures of before and hopefully after :)

Hi Mike. As you are in N. Humberside it may be worth a short trip to Reighton nursery just north of Bridlington. When I decided to go tropical (changed my mind after the fun of losing all my cordies last winter) I got loads of stuff at about ¼ of garden centre prices. My 2 Fatsias were £2 each 5 or 6 years ago. They'll be more now I know but at least they both survived the big freeze and a buying trip will certainly be worth the petrol.

A tropical looking, easy to grow annual is Nicotiana sylvestris. May be useful to fill gaps over the first season whilst things are getting established.
For flowers, consider pot grown bulbs such as Scadoxus multiflorus and Hymenocallis - these can then be stored under the stairs, in the loft or anywhere else frost free for the winter.
If you have a conservatory, then Strelitzia and Anigozanthos in pots.

Agapanthus, hardy ones - they're not really tropical, but look the part in with spiky plants.