Russell T Davies has stated that The Ark in Space is his favourite story, and, in viewing the new series as produced by Davies, it's easy to see why. While no new series episode bears an obvious relation to The Ark in Space (and certainly not any episode written by Davies), the driving force in the new series can be distinctly seen in Philip Hinchcliffe's debut story.
That driving force is humanity. Never before have humans been held up to as high regard as they are in The Ark in Space, and never has The Doctor been more complimentary. The Doctor's "indomitable" speech from Episode One is the most blatant example of The Doctor's sudden professing of his love of humanity, an attitude which he later confirms in Episode Three by calling humans "quite his favourite species". The way The Doctor cares for each frozen human (as he tells Vira, "What we're protecting (humanity) is too important"), even convincing his two human companions, Sarah and Harry, that they must stay on Nerva and defeat the Wirrn before even thinking of fleeing in the TARDIS.
The Doctor's love of humanity has been resurrected, most notably, in the David Tennant era. Tennant's Doctor has, on many occasions, enthused at how marvellous he thinks humans are (even quoting the "indomitable" speech in Utopia). The Doctor's love of humans also serves to set him apart from them. After years of mingling with humans, The Doctor is, perhaps for the first time since the William Hartnell era, truly an alien again.
The Ark in Space is as near to perfection as any producer can ever hope to achieve in his debut, and Philip Hinchcliffe has succeeded in starting his era off just right. Surely, these are the halcyon days of Doctor Who.