Be careful of following this advice, as you will pay for it.
Who you go to will depend on your level of trust and risk profile. If you don't do your homework and check out the travel agency (web or high street), then you won't trust them. If you are risk averse and revert only to the well-known names, then you will pay a premium.
On the subject of online versus high street, the high street agency is probably more likely to out of business than an established web agency (note the word "established" - with a proven track record), as the high street has rents and generally higher overheads.
Also, you can generally find insurance to cover risks (the agency themselves should be bonded, so you can always ask for evidence of their bond scheme).
In summary, you can increase your trust and reduce your risk by just doing a little checking and seeking the extra assurances.