We have carried out a photometric and spectroscopic survey of bright high‐amplitude δ Scuti (HADS) stars. The aim was to detect binarity and multiperiodicity (or both) in order to explore the possibility of combining binary star astrophysics with stellar oscillations. Here, we present the first results for 10, predominantly southern, HADS variables. We detected the orbital motion of RS Gru with a semi‐amplitude of ∼6.5 km s−1 and 11.5 d period. The companion is inferred to be a low‐mass dwarf star in a close orbit around RS Gru. We found multiperiodicity in RY Lep from both photometric and radial velocity data and detected orbital motion in the radial velocities with hints of a possible period of 500–700 d. The data also revealed that the amplitude of the secondary frequency is variable on the time‐scale of a few years, whereas the dominant mode is stable. Radial velocities of AD CMi revealed cycle‐to‐cycle variations, which might be due to non‐radial pulsations. We confirmed the multiperiodic nature of BQ Ind, while we obtained the first radial velocity curves of ZZ Mic and BE Lyn. The radial velocity curve and the O–C diagram of CY Aqr are consistent with the long‐period binary hypothesis. We took new time series photometry on XX Cyg, DY Her and DY Peg, with which we updated their O–C diagrams.