From previous experience going in at a 'local' level with a fraud involving £several thousand and having hand-held step-by-step paperwork, it was a complete waste of time ... had it not been for my bank it would have been lost forever - hope London is different.
You don't have a choice in the matter, unfortunately. It is not possible for members of the public to "leap frog" and take their cases to specialist units, unless it is prima facie too big for local investigators to handle - in which case, they will be the ones to refer it.
When harping on about policing, I only ever draw on my own experiences - I'd like to think if your case landed on my desk, I'd do a good job with it - but I'm not naieve enough to promise you that it'll always be the case wherever you go in London!
Frauds are a nightmare for investigators to prove; the sheer quantity of paperwork (through production orders, phone requests etc) is a nightmare, and the banks / mobile phone operators / eBay, etc, genuinely don't give a toss until the value is in the region of more than a few thousand pounds. The whole experience is like wading through treacle. It ends up taking months and tying up officers' time for a (usually) indefinite amount of time. The even sadder thing is that even if you do take the case on and make progress, by the time this huge bureaucratic machine has run its course, the fraudsters have usually moved on - especially with anything internet-based.
Unfortunately, since we don't have the resources to investigate everything as fully as we'd like, Fraud is not a priority crime anywhere - unless it's on a major scale - as far as I know. At a local level, it sits very much at the bottom of the heap, with Robbery, Serious Violence, Burglary and Domestic Violence all taking priority - to say nothing of rapes, murders and so on which are dealt with at a specialist level. It's not great, it's not right, but them's the breaks.
Personally, I always enjoyed investigating frauds - I took down an organised Nigerian gang scamming people out of properties across the UK last year, a travel agent ripping off hundreds of tourists by booking non-existent tickets, the accounts manager of a huge online poker company setting up fake commission accounts and creaming off the money, and have another interesting
sub-judice case involving the a manager for a major brewery defrauding the company out of tens of thousands coming up at court soon. Each of these cases took around a year from start to finish (but I was working on several cases at any one time).