The Adobe Creative Cloud Photographers package is £8.57 per month in the UK (
http://www.adobe.com/uk/creativecloud/photography.html), and well worth it.
You can get a 30 day trial of Lightroom (which is probably where you will do most of your processing - it is used to 'develop' RAW images to Jpeg (
https://lightroom.adobe.com/) before committing to the full plan.
Camera wise, it does depend on what you are aiming to shoot, and how 'serious' you are about it.
£400 is a relatively modest budget (fine for starting out though), and depending on what you are shooting you may see no improvement over your current bridge camera - you certainly won't be able to get any lenses with the reach it has (The built in lens is the equivalent of 24-1550mm lens - the 'longest' lens you can practically get for the Sony A mount is the Tamron 150-600mm lens, which is £800).
Where interchangeable lens cameras do show a marked difference over bridge cameras is when they are combined with 'wide aperture' lenses - this allows you to take shots where the subject is in sharp focus, but the background is out of focus and 'smooth'
EG
The problem is that, in general, wide aperture lenses are quite expensive (that was taken using the Tamron 70-200 F/2.8, which is £1100 new).
What people often start out with is a couple of general purpose lenses, often bundled with the camera and refereed to as 'kit' lenses - these are fine for normal shots, then add a wide aperture 'prime' lens (A Prime is a fixed focal length lens, rather than a zoom, which is variable focal length) - such as a 50mm f/1.8 as these are often relatively inexpensive.
Note that as DSLR tend to have much larger sensors than bridge cameras, this will give a more blurred background effect anyway, it's just more pronounced with a wide aperture lens.
My 'travel' kit, for example, an A6000 + 16-55 'kit' lens, 55-210 'kit' lens and 50 f/1.8 lens - new, this is over your budget (it doesn't help that prices have just gone up significantly with the weakening of the pound), but that is the sort of set up I would suggest as something general.
If you are not worried about lower light situations, then getting and older s/h A-Mount Sony is an alternative, which could be cheaper and possibly allow something like a 17-50 f/2.8 zoom as well.
Are you keeping the bridge? If so, you can concentrate on camera & a single higher quality lens, then use the bridge when you need longer focal lengths (longer focal length lenses are typically more expensive than shorter length lenses, as well as being nigger and heavier).
