I cannot see how the field can be treated as part of your home and eligible for main residence relief I'm afraid, especially since it was has been used by a farmer.
Even if you sold the house and the field together, you would still need to split the gain between the two in my opinion. The gain on the house will be exempt from CGT because it has been your main residence since you bought it. If any part of the gain on the house was taxable which it clearly is not assuming the total plot (excluding the field) is no more than half a hectare in size, the calculation would be based on the March 1982 value. Any increase in value between the purchase date in 1968 and March 1982 would be exempt from CGT
As for the field, if you sell it for £150,000 having paid £27,000 for it, you will make a gain of £123,000, £61,500 for each of yourself and your wife. There is no longer any form of taper relief and you won't in my opinion be able to claim that you were running a business by letting the field to the farmer. Had you run a business on the field, you would have qualified for entrepreneurs' relief and your gain would be liable to CGT at 10%. You can claim the costs of purchase and sale (legal fees, survey fees, stamp duty, selling agent fees) against the gain. The cost of any capital improvements can also be claimed.
I'm afraid there isn't much you can do to minimise the tax charge on the field other than not sell it in a tax year where you are a higher rate taxpayer. Having said that, even if you had no income, almost half the gain would be liable at the higher rate of CGT in any event.
There are two rates of CGT, 18% and 28%. The rate or combination of rates you will pay will be dependent on the level of your income in the tax year of disposal of the property. Assuming you sell the property in the 2014/15 tax year, one or other of the following will apply to each of you:
1 If your income in 2014/15 including the taxable gain is £41,865 or less, then all the taxable gain will be taxed at 18%.
2 If your income in 2014/15 excluding the taxable gain is more than £41,865, then all the taxable gain will be taxed at 28%.
3 If your income in 2014/15 excluding the taxable gain is less than £41,865 but more than £41,865 when you include the taxable gain, then part of it will be taxed at 18% and part at 28%.
The HMRC helpsheet HS283 here has more information on the main residence and CGT.
I hope this helps but let me know if you have any further questions.