The government's public-facing tech (gov.uk & related systems) is actually pretty world-leading and done in-house for a not extortionate amount, so it may be possible to form teams under the same organisation to develop internal software
That said though, those in government probably want to keep stuff under the table with WhatsApp and so probably would spend billions on contractors owned by their mates only to claim it's too expensive when it's nearly complete and scrap the whole thing, ideally with high cancellation payouts (this was the plan all along to look like they tried to do something while keeping the status quo)