Definitely get your own! I have had 4 house purchases using the bank's surveyor, the first 3 were homebuyers reports and all fine. The last survey for the most expensive, big and old house we have ever bought, we decided to play it safe and get a full building survey. Got it through the bank (tbh, at that time I didn't know there were any other options) and got a survey which was virtually useless (half the size of previous homebuyers reports, which cost hundreds of pounds less than this full survey). Spoke to bank, they said it would be fine so we took their word for it. Survey bascially said good house, no problems.
Soon after moving into the house we realised there were loads of problems that hadn't been picked up. We paid another £1000 for another building survey from a recommended surveyor. This survey was leagues apart from the old one and basically showed us we had around £25k of problems, including major ones like re-pointing everywhere (£8k), new garage and kitchen roofs, new oil tank etc etc.
We're now in the shit position of having to try to claim back money through the Ombudsman (can't afford to sue him, litigation lawyers are £250 per hour and apparently surveyors tend to drag these cases on for 12 months before settling)
Get a cheapo bank valuation and get your own survey done!!!
We used our own surveyor, recommended to us by family (as well as the bank valuation). I definitely think it was worth it - he spent hours in the property and the report was 20 pages. It was useful to us when doing building work as well as we knew where all the dodgy plaster etc was.
It wasn't really much more hassle - we found it a lot easier to get our own surveyor booked in than we did to get the bank's valuer booked in! And it wasn't much more £ either compared with the cost of getting the bank surveyor to do both (in fact I have a vague memory that it might have been a bit cheaper our way round)
Oh and I forgot to mention the most important thing which is that our surveyor picked up two major problem areas (drains and ground movement). I don't know if the bank's surveyor would have picked these up, maybe they would have on a full survey, maybe not.
I just feel that someone who relies on recommendations and word of mouth for their business is likely to do a better job than someone who is employed by the bank and so has a "captive market" iyswim. but do make sure you go with someone recommended.