The number of electric vehicles on the road in the UK is expected to rise quickly in the coming years, and this is likely to have an impact on the operation of the power grid. This paper first quantifies the consequences of allowing a completely electric fleet to charge freely, then considers whether there is a practical way in which the impacts can be mitigated. We predict that, with an entirely electric fleet, the UK power generation capacity would need to increase by 1/3. We show that it is possible to completely mitigate this with controlled charging, although substantial infrastructure would be required. However, we propose a simple scheme which could largely avoid the negative effect and does not require the creation of new infrastructure. We show that this reduces the projected increase in peak electricity demand by 80-99%.