Phew, warming up the fingers... here we go.
A bluefin angelfish will likely be a coral nipper, probably not the best idea for a mixed reef. Cauderns cardinals have very poor survival rates when wild-caught. If you can find tank bred ones they're much hardier. A PBT is an exceptionally demanding fish from a care standpoint. They're voracious eaters, exceptionally active swimmers, and need to be fed constantly. If not, their health suffers and they become very prone to developing ich. An auto feeder is a MUST when keeping PBT's. Rest of the fish would be fine. If I may suggest, have a look at Anthias and/or Pseudoanthias, a stunning schooling fish that would look great in a big tank like yours. Also don't forget reef safe fairy and/or flasher wrasses. Beautiful and active swimmers
Corals are all fine, all exceptionally easy species to keep
The shrimp are all fine choices. I'm not a big fan of hermits myself, but they may do better in a larger tank like yours with less territorial issues than they did in my little 65g. The Flame Scallop surely is a gorgeous species... Except their survival rate in captivity is dismal in tanks below say 200 gallons. Simple reason is that they're filter feeders and just can't get enough food from a small tank. They end up over-filtering out all their possible food sources and die. If you wanted a different clam-type organism, look up Tridacnid clams (Derasa, Crocea, Squamosa, or Maxima). They require SIGNIFICANT light, but are certainly gorgeous creatures.
Lastly my thoughts on the anemone. Rabbut is right in saying they need mature tanks, yet the key really is stability, and this is not necessarily tied to a time frame like one year. The reason he and most others will reccomend that one year mark is because it will take a new saltwater aquarist somewhere between 6-12 months to really get comfortable with the aquarium, its inhabitants, and especially care for the water quality. I know some fellow local aquarists who've been doing this for a decade or more who have managed to setup a tank and have an anemone thriving in it merely a month after rock was added. Then again, they have a decade of experience and knew exactly what to do... Hope that makes things more clear there. Also, were I to choose an anemone for a first-timer, I'd choose a bubble tip anemone. They're by far the hardiest decorative nems in the trade
A word about lighting. Your tank at 4x2x2 is quite a deep one (top to bottom). The deeper the water, the harder it is for the light to "punch" all the way down. And it's not quite a linear decrease in light with increased depth, it gets worse with depth. I personally have a 36x18x24" tank with dual 175watt halides. To give you some idea, I get about 350 PAR (a measure of photosynthetic available radiation) just below the surface, about 150PAR halfway down, and then around 100 PAR at the sand bed. So the initial dropoff is pretty significant.
Dual 150watt halides will certainly give you some good light and enough for all the corals you mentioned. If you ever wanted to branch out into something more difficult, you'd either have to switch to 250's, or add a few supplimental T5's. It would be good to ask you what you want to do for a hood for the aquarium? Will you use one? Or would you prefer an overtank luminaire that sits on top of the tank with legs on the sides? Or perhaps you'd prefer a pendant style system where they hang from the ceiling or from a shelving bracket on the wall? Important questions.
Halide tech in the UK is a little different than over here in the US. For reasons I've never understood, 175watt halides do not SEEM to have caught on there in the UK. 175watt halides are often electronically ballasted and therefore much more electrically efficient (they make less heat and more light than a magnetic ballasted 150). Also when considering halides, if you have a good head about you and a decent DIY sense, you can save yourself TONS of money by purchasing industrial ballasts/fixtures usually designed to light large spaces or for security lights and just replacing the lamps with aquarium lamps. Or if you'd rather go somewhere in between, and you want to use a hood, you can get a "retrofit kit" and safe a pretty-penny that way too. And lastly with halides, do not be dicouraged with buying used... In fact, be encouraged with the prospect. While lamps may have a shelf life of 2-3 years, ballasts can easily last decades, so buying used fixtures can save you lots without sacrificing reliablity/quality.
Lastly, T5's as rabbut said you'd need at least 4 54watters with individual reflectors (individuals are key) to keep those corals you listed. Again, if you wanted to branch out into more difficult corals, you'd probably want 6 54's. T5's have higher initial setup costs, but can save siginificant cash in energy costs over the years as they're way more efficient than magnetically ballasted T5's. They are however only barely more electrically efficient than electronically ballasted halides, and as such it's really the aquarist's choice making that decision. Also same thing applies with T5's as with halides; retrofit kits and buying used ballasts/fixtures can/will save you a LOT.
And one last thing, don't overlook the convenience of a sump. I've always used one on my saltwater tanks, so I may be biased, but I would never run a tank without a sump. The ease of waterchanges, place to hide equipment, place to dose, and the bonus of having that hidden-away refugium is so worth the hassle of setting it up IMO
Hope that helped
It may be cheaper to use a pair of 150W halides though from a lamp replacement perspective. New halide lamps cost £20 each, and need at most anual replacement from one Ebay seller. T5's are £30 each, and need replacing every 6 months. You are consuming an extra 84W with the 150W halides, or 9.5p a day more electricity... T5's are fractionally cheaper, but for an extra, say, £30-40 a year in running costs, you have a few more options for stocking open... It's a cost-vs-benefit trade-off
Think of a 150W halide and a 150W heater in that's locked on. You need that heater as close as possible to prevent too much light spread, but you need it far enough away not the heat the water. 
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