  We present 15-GHz follow-up radio observations of eleven Swift gamma-ray
burst (GRB) sources, obtained with the Arcminute Microkelvin Imager Large Array
(AMI-LA). The initial follow-up observation for each source was made in a fully
automated fashion; as a result four observations were initiated within five
minutes of the GRB alert timestamp. These observations provide the first
millijansky-level constraints on prolonged radio emission from GRBs within the
first hour post-burst. While no radio emission within the first six hours after
the GRB is detected in this preliminary analysis, radio afterglow is detected
from one of the GRBs (GRB120326A) on a timescale of days. The observations were
made as part of an ongoing programme to use AMI-LA as a systematic follow-up
tool for transients at radio frequencies. In addition to the preliminary
results, we explain how we have created an easily extensible automated
follow-up system, describing new software tools developed for astronomical
transient alert distribution, automatic requesting of target-of-opportunity
observations, and robotic control of the observatory.
