"For murder you have to prove [intent] that's hard to do with a mugging."
If, by that, you mean a need to prove an intent to kill, that is incorrect.
As per the CPS guidance, "The intent for murder is an intention to kill or cause grievous bodily harm (GBH)."
The CPS guidance for GBH is, 'The words "grievous bodily harm" bear their ordinary meaning of "really serious" harm...harm does not have to be either permanent or dangerous and that ultimately, the assessment of harm done is a matter for the jury, applying contemporary social standards.'