not significantly no, with some exceptions for sectors where the biggest cost is lots of minimum wage staff (so perhaps cleaning companies will hike prices for example)
I mentioned In the other budget thread about Nurseries, who are a sector that this will affect massively, due to very high staffing levels required in relation to turnover.
To give you my example of a Nursery I'm the Finance Manager for, being mindful of childcare costs I've kept fee increases to a minimum where possible and from 2010-2015 the fees have gone up £5 a day, from £30 to £35.
Now to cover this rise, a quick extrapolation this morning showed that by 2020 our fees will need to be over £55 a day to cover this wage cost....

the whole 'if we increase the minimum wage then inflation will rise up too and it will all be pointless' is usually a flawed right wing argument against the minimum wage... as is the scaremongering that it leads to massive job cuts
Agreed, for most small businesses with only a few staff, the costs aren't going to be exorbitant and things will just carry on, but for others it's going to have a massive effect.