... I had always been led to believe that they are more cost effective to run, offered constant hot water and also took away the tanks in the loft and also the cylinder in the airing cupboard giving us more room.
The latter - space saving - is, IMO, the only benefit of a combi.
As to your "constant hot water", well yes a Combi will provide a stream of hot water for as long as you need - but not very fast. With your cylinder, usage is decoupled from production - so your boiler heats the cylinder at whatever rate the system works at, and then you use it at whatever rate you want/the plumbing allows (great for filling baths).
With a combi you are heating the water as you use it - so you have a trade off between flow rate and temperature (and it gets worse in winter when the cold water is colder). To get even a moderate flow of hot water you need a boiler that's grossly oversized for running the heating - in my flat I have a boiler that's getting on for 30kW while the heating demand for a one bedroomed property with only 2 outside walls has a heating load of less than 10th of that (when I measured it). It's OK for washing up, having a shower etc, but filling the bath can take quite a long time. Because of the flow limitations, they are also not good in multi-occupancy dwellings - someone turns on a tap anywhere in the house and the shower goes cold.
The combi might not be "instant on" either. When you turn on the hot tap, instead of hot water coming out of the cylinder immediately, you have to wait while the boiler fires up and gets it's internal loop up to temperature. I timed it for the boiler in the house and from cold it can take 20s for the water to be flowing hot. Many modern boilers work round this with various techniques - such as having a small tank in the back of the boiler, or firing up the boiler every so often to keep itself warm. Once you do that, I can't help wondering how much of the supposed energy efficiency savings disappear
It is my opinion, and yes, only an opinion, that much of the popularity of combis is down to the people selling them. From the installer's POV they are simple to fit, and this in theory means they should be able to offer a lower cost - does all the saving get passed on ? Unless you've lived with both then you probably won't realise the differences until it's too late - and few people are going to pay to have the brand new boiler got rid of and their old setup restored. In any case, they'll be comparing a brand new system with one that may be 20 year old or more - which may hide some of the deficiencies of the combi in a comparative test. Since pretty well all new flats and small houses come with a combi, I reckon there's a whole generation out there who don't know the benefit of stored heat - hence they don't know to ask for better than a combi.
That makes it easy for the salesman to sell them another combi with the promise of constant hot water etc.
And don't forget, if you go back long enough, it used to be common to "put the hot water on" in advance of wanting (say) a bath, and turn it off again afterwards. So going back a a bit, it wasn't normal to have "constant hot water". If someone hasn't lived with a storage cylinder for a long time (eg they've had a combi), then they may well still remember the hassle of planning your hot water usage. Also, I suspect cylinders of old tended to be undersized and have slow recovery times - meaning a delay of possibly hours between consecutive baths.
Yes, I make no secret of my dislike of combi boilers.