Upvote:3
The inter-terminal shuttle at Gatwick is airside, and will take you to the other terminal without clearing border control. The shuttle takes about two minutes and will add nothing significant to your transit time. So the change of terminals makes no difference.
However you say you have to collect bags. I presume from this that you bags are not checked through to your final destination. According to Gatwick this means you will have to clear border control. This means your wife cannot automatically make transit without visa - and this would have been true even if you hadn't had to change terminals (link above). There are circumstances under which she can make a transit without visa, even if she has to clear customs - see this page (Although be aware that the details of the regulations may have changed)
If you do not have to collect your bags and clear border control then you will be fine. If you have to collect bags and clear border control she may need a visa. The change of terminal makes no difference.
Follow the links at this question to find out about visa requirements.