Not sure why the FL70 constraint at TIMBA was not published in the 3B STAR. In general aircraft should be able to achieve FL70 by the clearance limit.
Gatwick could be asking you to expedite descent before turning you downwind for 08R because of traffic approaching HOLLY or holding at WILLO. The constraint of 5000'or below to avoid the Heathrow MID SID applies further west near Billingshurst.