You can expect serious traffic congestion during most rush hours on the main A3 as commuters head south from London and Guildford. Otherwise the A3 is relatively light in traffic terms out side the rush hour period. The A281 is also busy with coast traffic on Friday and Sunday nights. Friday as weekenders and commuters head to the coastal areas and Sunday as the weekenders return.

Rail ~ north/south and east/west choice 
Key: Train lines shown as a black line with red squares as stations.
As can be seen from the map above Waverly is served by two links to London. The first is the Portsmouth to London line that passes through Worrmley, Milford and Godalming.   The second is the Farnham to London line for south west trains.  Commuters for destinations north of London can get services out of Guildford but these services are more weekly than daily. Visit www.railtrack.co.uk for further information.  Most stations have car parks adjacent to them, but these can fill quickly and are generally expensive.  

Air ~ both London airports nearby
Waverly has easy access to the M25 via the A3 to Ripley and therefore is in easy reach of Heathrow. An good estimate of average time from Godalming  to Heathrow is 60-90 minutes. Mind you the M25 is renowned for making airport journey times much much longer so if you are heading to Heathrow you would be wise to allow twice that amount.  Gatwick airport is a much more leisurely drive, if you want to brave the M25 you can head across country  through the country lanes via Ewhurst to Charlwood, this is a pleasant drive in the Spring, Autumn and Summer months but you would be wise to avoid this on icy snowy days as the roads are not cleared as well as the main roads. Without traffic delays you can get to Gatwick from Godalming in about 60-75 minutes but as always allow more time for unexpected problems. See www.heathrow.co.uk and www.gatwickairport.co.uk  for more information.