Your requirements are slightly contradictory in terms of what's available on the market.
If your requirements were primarily to print, copy or scan A4 documents, I would have no hesitation in suggesting a multifunction laser printer, either monochrome or colour. For example:
http://www.ebuyer.com/product/220889
http://www.ebuyer.com/product/192095
http://www.ebuyer.com/product/226334
I can't specifically recommend any of these, but I do have a Samsung colour laser and would certainly buy another Samsung one if I needed it.
Laser printers offer excellent quality printouts for documents, or even casual photo prints.
A3 sized laser printers, however, start at more than £1000. If A3 printing is hugely important, you've no option but an A3 inkjet printer if you want to remain within your budget. It would however be a bit of a waste to use an A3 inkjet for A4 document printing, and you may find the inks expensive.
An inkjet printer will also be necessary if you want photo-quality printouts at greater than 10x15cm (4x6") size.
A cursory search revealed a handful of multifunction A3 inkjets made by Brother which come in over your budget. e.g.:
http://www.ebuyer.com/product/255103
A non-multifunction A3 inkjet would be around £170 from Ebuyer. (I'd guess about £200 in a physical shop).
Your third option is a dye sublimation printer. These produce good photo prints, usually at a fixed 10x15cm size. (Hence my above comment about inkjets being necessary for greater than 10x15cm.) They are pretty single-purpose machines but are often very portable and suitable for standalone use with a digital camera.
I suspect your ideal solution will combine two separate printers. You could also consider buying one printer that will serve you well most of the time and then buy high-quality prints from a third party supplier when necessary. There is no shortage of shops offering A3 laser prints, bindings, portfolio cases and the like, if required, at reasonable rates. Photo prints can be ordered in all sorts of sizes and formats these days, too.
If you must have just one printer, an A3 multifunction inkjet seems the best option, but seems very extravagant if you don't often need either A3 or high-quality output.
Laser printers offer the lowest cost-per-page for black-and-white printouts, and are pretty close to inkjets for the cost of colour output. They also tend to produce sharper, more consistent results than an inkjet. The toner has a distinctive slightly shiny appearance on the printouts, when held in raking light. Photo prints will be noticeably "dotty" when viewed up close (like a newspaper, but with smaller dots) but will also have vibrant colour reproduction.
Dye-sublimation printers excel at producing continuous tone images (i.e. photographs) because the image is not made up of tiny dots or ink droplets. A good quality inkjet may offer such a high resolution printout that the use of droplets becomes a non-issue and the dye-sublimation printer loses its selling point. Dye sublimation printers are relatively costly to run and typically require special media packs that contain both paper and dye, providing an exact number of prints.
Inkjets are the most versatile type of printer available to you. You can put practically anything through an inkjet as print media, especially if it has a straight-through paper feed. Most of the "special" print papers you can buy in the shops are designed for inkjets. I once cut out an A4-sized piece of aluminium foil and printed on that in an inkjet. (It worked, but the ink didn't dry properly.) By contrast, laser printers are very fussy about what you put in them, and are easily damaged by inappropriate print media (e.g. inkjet label sheets, photo paper), requiring expensive repair or replacement components.
Inkjets can be expensive to run, especially high-end ones (and A3 models might fall in that bracket). The ones that take the cheapest ink cartridges can compete with lasers on cost, but not necessarily on quality.
I hope I haven't overloaded you with information, or been too vague about specific models to look at! Hopefully this will help you to make an informed decision.