Successive governments have long scapegoated immigrants for social ills brought about by the powerful, but none have made it so core to their mission as this one.

In concert with a mendacious, bigoted rightwing press, immigrants have been blamed for stagnating wages caused by austerity and weakened unions, a housing crisis caused by a failure to build, a lack of secure jobs caused by rapid deindustrialisation, and strains on public services caused by ideologically driven cuts. And yet, without migrants, those services would collapse within hours. This is a fact admitted by this migrant-baiting government, but sadly in deed rather than in word. It has just been revealed that the government will relax immigration rules to allow more non-EU doctors to come to Britain because of shortages of medics – shortages that the Tories are themselves responsible for.

The chutzpah is quite something. The NHS is in the midst of a general staffing crisis – there are nearly 42,000 nursing vacancies and more than 11,500 doctor vacancies – because of deliberate actions by the government. Bursaries for trainee nurses and midwives have been cut. Salaries have been frozen, in practice meaning a real terms pay cuts. The NHS has suffered its worst funding squeeze since its foundation seven decades ago, placing ever-growing stress on staff. Media and government attacks – for example, during the junior doctors’ strike – have demoralised hard-pressed nurses and doctors. No wonder so many are deterred from training, or plan to flee the profession: indeed, two out of every five GPs intend to quit in the next five years, the highest on record and twice the level in 2005.

So the Tories plunge the NHS into this artificial crisis, and then go cap in hand to the very migrants they have been demonising and blaming for our recent problems. It was already the case in the David Cameron era that one in four nurses had to be recruited from abroad because of shortages. Now they’re begging migrant doctors to plug the holes they have themselves created.

But here is an opportunity for those of us who oppose the scapegoating of migrants. Polling shows that anti-immigration sentiment in Britain has fallen significantly over the past few years. That’s not to be complacent, especially given Hope Not Hate’s recent research suggesting that hostility to migrants has increased among a hard core of the electorate. Yet the case for the fact that our broken social order, rather than migrants, is responsible for contemporary problems now has a much more receptive audience.

One of the mistakes made in the past is to reduce the benefits of migration to crude economic contributions: for example, to say that migrants put in more than they get back. Instead, the case has to be made with humanity: for example, extolling the contribution of the doctors and nurses who care for us and save our lives. The government has overreached in its migrant baiting – and the opportunity to turn the conversation round must be seized.

• Owen Jones is a Guardian columnist