I've been cycling for four years now in Oxford, so I thought I'd look at the costs involved.
In total I've spent £1020 on cycling over the four years, which works out at £255/year or just under £5/week. That includes three bikes - two secondhand three-speeds bought for £110 each (the first was stolen the day I bought it) and a fully-fitted 8-speed city bike bought new online for £295 - assorted parts - a pannier bag, bike locks, brake blocks, a replacement tyre, a replacement shifter, an extra lockup loop for the front garden, and the WeeRide child seat - a £55 maintenance workshop, and regular servicing.
Barring theft, I expect my current bike to last several years (and I still have a three-speed for when we need a spare bicycle), though we might need a tagalong or a trailer or other new child-carrying gear at some point.
For comparison, an annual Oxford Smartzone bus pass costs £435/year. (Though that covers trips as far out as Kennington, Wheatley and Cumnor, which are further than I'd cycle on an everyday trip - and, with the little one, I've done some intra-Oxford bus trips anyway over the last year.)