There's a few questions to ask yourself regarding implants:
What was the original reason of the loss of teeth? Do you have any active gum disease?
I don't know your specific details, but it's rare that the loss of a large number of teeth is caused by a single event or traumatic event alone. The problem is a lot of patients do not know the real reason why they have lost their teeth - either because the dentist hasn't bothered really explaining the condition (common amongst time strapped NHS dentists) or that patient refuses to accept the cause of the loss of their teeth was ultimately their own (common amongst people that think the dentist is fobbing them off or don't like being 'told off' for inadequate cleaning- the reason usually being gum disease - which is the result of inadequately cleaning your teeth and gums loosens teeth, or tooth decay, if you're a chronic snacker / drink a lot of sweet drinks or graze a lot) . If the original issue isn't addressed, then implants will not work either. Implants are held in by the bone and gums that hold in your normal teeth so if you have gum disease, then your implants will fall out too.
The cost of an implant, certainly in the Yorkshire region, is around £2-2500 per implant with the crown. Some dentists will try and make the price more appealing by quoting £1000, but that would just be the surgical aspect of the implant (the titanium rod itself). After 3-6 months this needs to have a crown (single tooth) or bridge (multiple teeth) cemented on top of it which will make it up to £2000. Depending on what you've got left, it isn't necessarily a case of you need an implant for every single tooth gap. If you've got a single gap, then a single implant is the way to go. If you have a large gap, then you be able to have 2 implants and a bridge. If you have no upper teeth, then 4 implants with a denture or bridge may be possible. It starts to get expensive when you have sound teeth breaking up the gaps as then you will need implants on each side of the sound teeth and some dentists may recommend to get rid of any poor prognosis teeth and recommend full implants on the top.
Be careful when selecting dentists that place your implants. Word of mouth certainly will tell you how NICE a dentist is, but it certainly doesn't tell you how good they are. If you want implants, I'd recommend asking your dentist for a recommendation to where to go. Most should know somewhere pretty reasonable. I wouldn't just look it up at google - you'll find the one with the nicest websites, but not necessarily anyone any good. Just in the same way I wouldn't know what makes a good electrician or plumber, the public will not know a good implant dentist. Ask someone in the profession for a recommendation.
Are you an NHS or Private patient? If your check up is a 5 minute in and out job, there may well be several un addressed issues that need fixing far before considering implants. I have some issues with NHS dentists that I feel a majority do not spend enough time looking or explaining problems - I would recommend a private dentist as with anything in life you get what you pay for. Again not to put a downer on the issue but there are some terrible private dentists as well, a private fee is no guarantee of quality.
Implants are being a bit of a fad where there is no specialist training or exam required as such to place them - this may be introduced in future but certainly isn't the case currently. If someone has a masters degree in implantology that is a great sign but strictly speaking someone could have done a weekend course and be providing implants so you have to be aware of this.
In regards to 'dental tourism' - no dentist in the UK would recommend this. It's not a case of being 'jealous' that you're taking your business elsewhere where they can undercut our prices - the after care you need can be substantial if things go wrong - implants can get infected, painful, loose, and you really want someone local. Even referring someone to have implants on the other side of the country is difficult - we've had many a patient turn up who decided to go somewhere 'cheaper' and we then face difficulty as general dentists in knowing how to deal with their implant related problems.
From the sounds of your problems I'd strongly recommend getting all your crowns investigated if you decide to invest in any implants - most private dentists would be happy to do this - NHS not so much sadly. Getting recurrent infections (and the fact you have numerous crowns) suggests that you have underlying problems. This may well factor into the overall plan if you decide to get implants as you may decide that you'd prefer to get these poor condition teeth extracted. But like I said before, you need to make sure all your problems (gum disease being the main one, and then tooth decay) have been addressed. If you don't already go and see a dental hygienist, then please ask. Most implantologists will refuse to see patients if the hygienist hasn't cleared them first so this is a great step to make sure your gums are in check. If the hygienist does not recommend interdental brushes (and does not demonstrate them to you in your mouth) , doesn't do a pocket chart, and doesn't use an ultrasonic scaler, find someone else.
Feel free to PM if you wish.