The Tories have set targets which have been comprehensively missed for several years anyway. A target and a limit won't work. And if you believe those that hire seasonal workers, thousands of British people won't do them. They seem adverse to manual labour jobs, thinking them beneath them.
I don't believe Brits are averse to doing those jobs, if the wages were realistic. Heck, I see Brits doing hard, low-paying jobs all over the place down here in Cornwall. We have lot of those jobs down here.
I do believe that firms know they can treat immigrant workers in a way that Brits would baulk at... refusing them their rights, forcing them work in unsafe environments, forced unpaid overtime... I know a few firms round here that have a reputation for being appalling employers - really, really abusive. The churn in these places is phenomenal. But they know there are always desperate people here to replace the outgoing staff.
The trend as I see it is that Brits are accustomed to safe working conditions, are asking for realistic wages relative to the area they live in. Immigrants are happier it seems to live five to small bedroom - we see now in certain parts of the country unscrupulous landlords putting 10+ tenants in a 3 bedroom house...
Yes I think there are situations that Brits won't accept. I don't think it's down to "aversion to hard work", but a combination of factors. We aren't used to working in unsafe workplaces for pennies; eastern Europeans probably are.