Some later settlements - e.g. at Wroxeter - were based on Roman towns. Others, like Carlisle, maintained a continuous occupation until the Norse raids. It is more true though to say that Roman stone was pilfered for all kinds of uses, especially up at Hadrians Wall which was several times taller than the present paltry remains.
However, the resettlement of Roman towns (for example Chester, Colchester, Bath, Exeter, York, Cirencester) tended to be a later trend by which time their Roman artefacts were either buried, ruined, pilfered, or what have you. The Saxons did not use Roman money, in fact their use of any money was limited, until later kingdoms when the Saxon kings issued sceats (silver pennies) with a combination of their own image on one side for propaganda purposes, and Christian symbolism on the reverse, usually a cross.
The Saxon and Roman cultures had very little in common, and Roman artefacts tended to be viewed with suspicion for a long time. The closest they came to Rome was the monastic system, and later on, visits to Charlemagne and various Popes, but that wasn't for a few hundred years after the Romans left Britain.