A group of five were seen fighting at around 8.30am in Eglantyne Avenue and William Morris Way, with witnesses saying they had seen a blade.
At the scene, police arrested a 19-year-old man from Newcastle, a 39-year-old man from Birmingham, a 44-year-old woman and 33-year-old man – both from Swindon – on suspicion of affray.
They were all taken to custody at Gablecross for questioning.
Insp David Tippetts said: “Residents will see a heightened police presence in the area this afternoon as we continue with our enquiries but please be reassured that we have made four arrests within hours of the initial report.
“No doubt local residents will be concerned to hear of incidents of this nature taking place in their neighbourhood on a Sunday morning – we would urge anyone with information, including any dash cam or CCTV footage, to get in touch via 101 and quote log number 74 of today. Any information could be significant to our investigation.”