To get the smoothest coat of paint you can get with any paint, thin it. If you're using a water based paint, thin it a bit with water. Oil based paints are thinned with white spirits (paint thinner or mineral spirits).
Thinning increases the drying time, thereby allowing the paint more time to self level. The reason why brush strokes are the curse of DIY'ers is that DIY'ers don't seem to realize that solvents are evaporating from the paint in the can all the time the can is open, and they'll use the same can of varnish (or whatever) for small projects for years on end. Before long, they end up with a product that's too thick to self level by itself, and by that time they've forgotten how thin and easy to spread smooth it was when they bought the can.
For best results, take the door of it's hinges and paint each top horizontal surface one at a time with a small roller. This will allow you to thin your paint (for a streak free finish) without concern that the paint will sag as it's drying (which is what happens if you thin too much and then paint a vertical surface).
Also, in my view, it's best to take the hardware off the door and reinstall it after the paint is dry.
If you want to paint a vertical surface, then buy a paint conditioner like Floetrol for latex paints and Penetrol for oil based paints, both made by the Flood Company here in North America. No doubt the UK has an equivalent product sold under a different name. Basically, these are low volatility high viscosity solvents that will slow the drying time of the paint without lowering the viscosity of the paint so that it won't sag as it dries on vertical surfaces.
Just remember that it's really the job of the paint to self level, not the job of the brush to put it on so smooth it doesn't need to. BUT(!!!), for a paint to self level well, it has to be thin enough so that it can flow easily for a long enough time so that brush strokes will flatten out by themselves, and that generally means thinning it.
Also, keep in mind that the more you thin a paint, the smaller the film thickness it will dry to, so compensate for thinning by applying an additional coat or two.
PS:
When you see the words "Do Not Thin" on a can of any paint or varnish, you need to understand exactly what those words mean. It means that the company making the product cannot meet the stringent government VOC requirements in it's products, and has resorted to the MOST EFFECTIVE WAY of reducing the amount of VOC's that evaporate from it's product as it dries... and that is by simply putting less VOC's in it at the factory. That is, they sell it thicker so that less solvent evaporates from it, and therefore meets the stringent government VOC requirements. So, "Do Not Thin" really means "Listen mate, we can't sell this stuff unless it meets government air pollution regulations, and the only way we can get it to do that is by putting less solvent than required into it when we're making it. That way, less solvent evaporates from it when you use it. Officially, we're telling you not to thin it, but what you do with it is entirely and completely up to you since you're not regulated by the same rules that we are. If you thin it, and it seems to work much better when thinned, then hey, more power to ya."
Certainly, all of you will realize that you have little to loose and much to gain by pouring off a small amount of the product with those words on the can into a smaller container, thinning that poured off amount, and seeing if it works better for you than the stuff that's in the can.
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