If you check your browsers developer tools network tab, you'll see that the browser first makes some sort of authentication request to get a JWT access token.
then it makes the actual request to get the json data.
You can emulate the whole request process with a flow like the example below :
[{"id":"1c44140cb8acf2cb","type":"inject","z":"5847b7aa62131d37","name":"","props":[{"p":"payload"}],"repeat":"","crontab":"","once":false,"onceDelay":0.1,"topic":"","payloadType":"date","x":160,"y":640,"wires":[["6da13aa2886382d1"]]},{"id":"b7762aa66de6a566","type":"http request","z":"5847b7aa62131d37","name":"auth req","method":"POST","ret":"txt","paytoqs":"body","url":"https://authwebservice.cardiff.gov.uk/AuthenticationWebService.asmx?op=GetJW","tls":"","persist":true,"proxy":"","authType":"","senderr":false,"x":400,"y":700,"wires":[["682b5c419c834422"]]},{"id":"33fc229af1bd9858","type":"debug","z":"5847b7aa62131d37","name":"","active":true,"tosidebar":true,"console":false,"tostatus":false,"complete":"true","targetType":"full","statusVal":"","statusType":"auto","x":630,"y":780,"wires":[]},{"id":"6da13aa2886382d1","type":"function","z":"5847b7aa62131d37","name":"","func":"msg.headers = {\n \"Content-Length\": \"284\",\n \"Accept-Encoding\": \"gzip, deflate, br\",\n \"Referer\": \"https://www.cardiff.gov.uk/\",\n \"Origin\": \"https://www.cardiff.gov.uk\",\n \"Content-Type\": `text/xml; charset=\"utf-8\"`,\n \"Sec-Fetch-Dest\": \"empty\",\n \"Sec-Fetch-Mode\": \"no-cors\",\n \"Sec-Fetch-Site\": \"same-site\",\n \"Pragma\": \"no-cache\",\n \"Cache-Control\": \"no-cache\"\n}\n\nmsg.payload = `<?xml version='1.0' encoding='utf-8'?><soap:Envelope xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xmlns:xsd='http://www.w3.org/2001/XMLSchema' xmlns:soap='http://schemas.xmlsoap.org/soap/envelope/'><soap:Body><GetJWT xmlns='http://tempuri.org/' /></soap:Body></soap:Envelope>`\nreturn msg;","outputs":1,"noerr":0,"initialize":"","finalize":"","libs":[],"x":260,"y":700,"wires":[["b7762aa66de6a566"]]},{"id":"682b5c419c834422","type":"xml","z":"5847b7aa62131d37","name":"","property":"payload","attr":"","chr":"","x":530,"y":700,"wires":[["24b162b725bfb0a2"]]},{"id":"24b162b725bfb0a2","type":"function","z":"5847b7aa62131d37","name":"","func":"let access_token = JSON.parse(msg.payload[\"soap:Envelope\"][\"soap:Body\"][0].GetJWTResponse[0].GetJWTResult).access_token\n\nmsg.payload = {\n \"systemReference\": \"web\",\n \"language\": \"eng\",\n \"uprn\": 100100073989 // code for address ?? you need to find it from browser\n}\n\nmsg.headers = {\n \"Authorization\": `Bearer ${access_token}`\n}\n\nreturn msg;","outputs":1,"noerr":0,"initialize":"","finalize":"","libs":[],"x":260,"y":780,"wires":[["b091cd6df0893112"]]},{"id":"b091cd6df0893112","type":"http request","z":"5847b7aa62131d37","name":"WasteCollection req","method":"POST","ret":"obj","paytoqs":"body","url":"https://api.cardiff.gov.uk/WasteManagement/api/WasteCollection","tls":"","persist":false,"proxy":"","authType":"","senderr":false,"x":440,"y":780,"wires":[["33fc229af1bd9858"]]}]
The data is in msg.payload.collectionWeeks
One small problem is that you have to make a request of your real postcode and address (from the browser) and see in its dev tools the uprn
code. Use that in the Function node to get the correct data relating to your address.