I too have been caught by these calls. In September when I was expecting a very important message my phone rang off after three rings, before I could reach it. Using 1471 I called back the 0870 number quoted.
It turned out to be an auto-dialling system operated by a telesales company. If the battery hens don't pick up these calls fast enough the system rings off, hence my missed call. Any subscriber anxious enough to call back, as I was at that time, therefore pays the sales company for pestering him/her with calls that should not have been made anyway as we're listed with the Telephone Preference Service.
Incidentally an effective way of stopping these before we signed up with TPP two years ago was to write to the registered office of the offender and state that you do not want these calls and further calls would be deemed to be hire of your electronic apparatus at the rate of £25 per call. (None of your 8p/min nonsense here, then).
There was a repeat call about six months later. My bill for £25 was ignored until I followed it up with a claim via the Small Claims Court. They paid up before the hearing and we've had no problems since.

I'm of the understanding the companies using ACE (Automated Calling Equipment) have to ensure that no more than 3% of calls are not answered by their staff.

They can't leave missed calls on your Caller Display from anything as high as an 0870 number (so 0844 and 0845 would be ok)
If you made the mistake to ring them back, then you can inform them to remove you from their list otherwise you'll take it further.

This is Ofcom regulation now and is classed as nuisance/silence calls under the Communications Act.  Companies like Argos, as we all know just love 0870 numbers, actually leave an 0845 number when doing their annoying calling.

This is related to Automated Calling but I guess most (if not all) applies to non automated calling when the companies' staff actually dial it themselves and leave a missed call.

This applies only to UK companies.  Any company outside the UK, unfortunately, could possibly get away with it scott free hence why more and more companies are 'international' now when they ring you.

As for small claims court, it could be possible I would have thought to try that route because if they're found guilty by Ofcom the fine would be much more substantial and could see them stopped from making other calls.  This and bad publicity (ofcom release investigations on their website) could be bad for the business so paying up via the small claims court would be easiest/cheapest/quietest way to stop such action.

On a personal note, I don't like these calls and I would have preferred Ofcom to ensure that freephone numbers are left so any missed calls, etc are left at their own expense and not ours (for those stupid enough to call back).

Re unwanted sales calls, faxes, emails:
This happened three or four years ago and related to unwanted faxes, we used to have a separate line.
I first faxed the company concerned and asked them to desist.
When this did not work with one persistent offender I wrote to the company secretary at the registered office with a copy of the fax request, roughly as follows:

I have previously asked your company to cease and desist from marketing phone calls and fax messages. A copy of my request is enclosed.
Yesterday a further fax (your ref ----) was received despite this request.
Take notice that your transmission of further sales communications will be deemed to be hire of my electronic equipment and associated administrative services, for which I charge £25 per communication.
In sending any such communication in future you will be deemed to have accepted this hire charge and will be invoiced accordingly. Please be in no doubt that I shall enforce payment of such invoices in court if necessary.
To avoid further inconvenience to me and expense to your company I should much prefer if you would remove my details from your marketing lists as I have asked.

When no payment was forthcoming I took proceedings via Small Claims. I don't remember the cost, it might have been £9 or so. The firm paid up a week after receiving the summons and I was able to cancel the action and have the fee refunded as the hearing was still four weeks away.
Had the case gone to court I don't know if I would have received an award or not although the helpful court staff seemed to think I would win. (Amazing how many people are annoyed by these calls). My object of course was to stop this firm's harassment and this method succeeded.
Thanks again for this super site. I used it yesterday to thwart a hotel group's 0870 system which keeps one hanging on while they drivel about meeting the needs of their guests ...